[GalFisk] The Cake List (a Jennings puzzle)

[GalFisk]

First, Darbishire told Jennings and all his other classmates at the Linbury Court boarding school that they would be getting a big slice of cake each.
Then, the classmates saw that they'd only be getting a tiny sliver of cake each. Darbishire blamed his grandma for this, and Jennings blamed geometry.
Then, they saw that they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster.
Then, Darbishire and his roommates thought they'd be getting a giant slice of cake each. Darbishire thanked Jennings for this, and Jennings thanked the matron.
Then, Darbishire thought they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster.
In the end, Darbishire and his roommates got a giant slice of cake each.

What happened?

This is another puzzle based on the Stompa plays in norwegian radio, again based on the Jennings books by Anthony Buckeridge. The classmates are HTM, all others involved are HAM/F.

[doriana_]

Is there just one relevant cake? More than one? Is the cake they get at the end the same one that Darbishire told them about in the beginning?
Did Darbishire's grandma send the cake? Make the cake?

[GalFisk]

Is there just one relevant cake? No. More than one? Yes. Is the cake they get at the end the same one that Darbishire told them about in the beginning? No.
Did Darbishire's grandma send the cake? Yes, one of them. Make the cake? No, explore.

[BitterLemonCurry]

Are the "classmates" and the "roommates" meant to be different groups of kids?
Were there two relevant cakes? three? more?
Did the headmaster confiscate cakes? ban eating cake? have cakes destroyed?

[GalFisk]

Are the "classmates" and the "roommates" meant to be different groups of kids? Yes.
Were there two relevant cakes? This. three? But this is also relevant. more?
Did the headmaster confiscate cakes? ban eating cake? No to both. have cakes destroyed? Not exactly, but...

[doriana_]

Did the headmaster eat one of the cakes?

[GalFisk]

Did the headmaster eat one of the cakes? Yesish, explore.

[Sundowner64]

Should there have been three cakes? Did Darbishire's grandma sent three? two? one?
Did the CakeForTheClass (let's call it this way to distinguish) ever arrive at the school? Was it sent by Darbishire's grandma? taken to the school by Darbishire? by someone else? Was it intended to be shared with the class? Was it, eventually? Did someone else take it away? eat it?
Did the CakeForTheRoommates ever arrive at the school? Was it sent by Darbishire's grandma? taken to the school by Darbishire? by someone else? Was it intended for Darbishire's roommates? Did they get it, eventually? Did someone else take it away? eat it?
Are both "cake events" connected?

[GalFisk]

Should there have been three cakes? No. Did Darbishire's grandma sent three? two? one? This.
Did the CakeForTheClass (let's call it this way to distinguish) ever arrive at the school? Was it sent by Darbishire's grandma? Yes to both. taken to the school by Darbishire? by someone else? By the mailman, but irr. Was it intended to be shared with the class? Yes. Was it, eventually? No. Did someone else take it away? Not "away", but... eat it? Yes.
Did the CakeForTheRoommates ever arrive at the school? It was made there, but irr. Was it sent by Darbishire's grandma? No. taken to the school by Darbishire? No. by someone else? The matron took it tot he boys. Was it intended for Darbishire's roommates? Not entirely. Did they get it, eventually? Yes. Did someone else take it away? No, but... eat it? No.
Are both "cake events" connected? Yes.

[Sundowner64]

Did Jennings eat the CakeForTheClass? Darbishire? a classmate? the matron? the headmaster?
Did the mailman hand over the cake to Darbishire? to Jennings? to the headmaster? to someone else?
Did Darbishire take the job to cut the cake into slices for the classmates? Jennings? someone else?
Relevant how many classmates were there? more than 5? more than 10? more than 15? more than 20? more than 25? more than 30?
Was the one who cut the cake mistaken about the number of slices required? Was the cake ever cut into slices?

[GalFisk]

Did Jennings eat the CakeForTheClass? Darbishire? a classmate?No tl all. the matron? the headmaster? Both ate 1/4 of it.
Did the mailman hand over the cake to Darbishire? to Jennings? to the headmaster? to someone else? To a teacher, who then handed it to Darbishire, but irr.
Did Darbishire take the job to cut the cake into slices for the classmates? Jennings? Jennings tried, but...someone else? No, but OTRT.
Relevant how many classmates were there? more than 5? more than 10? more than 15? more than 20? more than 25? more than 30? Yes, 36 all in all.
Was the one who cut the cake mistaken about the number of slices required? No. Was the cake ever cut into slices? Yes, but explore.

[Sundowner64]

So the task was to cut the CakeForTheClass into 36 equal pieces? Did Jennings start to do it? but was not able to finish? Did he start with too big pieces? Did the cake just turn into crumbs from being cut so small? Is the shape of the cake relevant? was it round? long? flat? high? wide? narrow? a very unusual shape?

[GalFisk]

So the task was to cut the CakeForTheClass into 36 equal pieces? Yes. Did Jennings start to do it? but was not able to finish? Yes to both. Did he start with too big pieces? Not too big. Did the cake just turn into crumbs from being cut so small? No, but it would have, if he had continued. Is the shape of the cake relevant? was it round? long? flat? high? wide? narrow? a very unusual shape? Round, flat, and small.

[BalinTheDwarf]

Was the cake cut across the horizontal center at any point (i.e. into a top & bottom half, and such)?

[GalFisk]

Was the cake cut across the horizontal center at any point (i.e. into a top & bottom half, and such)? No.

[Sundowner64]

Did Jennings first cut the cake into halves, then the halves again into halves (thus, quarters), then again and again, which would have ended up in 32 pieces? so, it became clear at some point that it is impossible to get 36 pieces of equal size?

[GalFisk]

Did Jennings first cut the cake into halves, then the halves again into halves (thus, quarters), Yes. then again and again, which would have ended up in 32 pieces? Good thought, but no. so, it became clear at some point that it is impossible to get 36 pieces of equal size? No, but something relevant became clear.

[BalinTheDwarf]

Did Jennings cut the cake into pieces smaller than quarters? Did he cut it into eight pieces? Sixteen?

[GalFisk]

Did Jennings cut the cake into pieces smaller than quarters? No. Did he cut it into eight pieces? Sixteen?

[Sundowner64]

Did Jennings cut the cake into quarters? and then realized that he would not succeed when he continues this way? or someone else realized it?
Did the headmaster and the matron get one of the quarters? Relevant what happened to the remaining quarters?
Did the headmaster and the matron expect to get a piece of this cake? Did Jennings offer it to them? Because the pieces were already so small that it would not have made sense to cut them further?

[GalFisk]

Did Jennings cut the cake into quarters? Yes. and then realized that he would not succeed when he continues this way? or someone else realized it? Yes to both.
Did the headmaster and the matron get one of the quarters? Relevant what happened to the remaining quarters? Yes to both.
Did the headmaster and the matron expect to get a piece of this cake? No.. Did Jennings offer it to them? Yope, explore. Because the pieces were already so small that it would not have made sense to cut them further? No.

[doriana_]

When Jennings cut the cake, was the headmaster present? the matron? the classmates?
Are Darbishire and Jennings roommates?

[GalFisk]

When Jennings cut the cake, was the headmaster present? the matron? DOYD of "present". the classmates? Yes.
Are Darbishire and Jennings roommates? Yes.

[doriana_]

Does the headmaster see Jennings cut the cake? Does the matron?
Relevant where Jennings cuts the cake? If so, indoors? outdoors? in the classroom? in the dining hall? in the dorms?

[Sundowner64]

Were the remaining two quarters also eaten? by Jennings? by Darbishire? by someone else?
Were they thrown away? get destroyed? were stored for later? did the dog steal them?

[GalFisk]

Does the headmaster see Jennings cut the cake? Does the matron? Probably not, but...
Relevant where Jennings cuts the cake? If so, indoors? outdoors? in the classroom? in the dining hall? Yes, here. in the dorms?

Were the remaining two quarters also eaten? by Jennings? by Darbishire? by someone else? Yes, this.
Were they thrown away? get destroyed? were stored for later? did the dog steal them? No to all.

[doriana_]

Does the matron perceive Jennings cutting the cut with any of her senses?
Does someone tell the matron that Jennings is cutting the cake? tell the headmaster? Does the matron tell the headmaster?
Was having the cake against the rules? cutting the cake?

Were the remaining two quarters eaten by a classmate of Jennings and Darbishire? by another student? by a staff member?

[GalFisk]

Does the matron perceive Jennings cutting the cut with any of her senses? No.
Does someone tell the matron that Jennings is cutting the cake? tell the headmaster? Does the matron tell the headmaster? No to all.
Was having the cake against the rules? cutting the cake? No to both.

Were the remaining two quarters eaten by a classmate of Jennings and Darbishire? by another student? by a staff member? This, two staff members.

[doriana_]

Do we need to know more about the staff members? Are they H/A/M? F? Are they teachers?
Do the other two staff members get the cake from Jennings? from the matron? from the headmaster?

[GalFisk]

Do we need to know more about the staff members? Yes. Are they H/A/M? Yes, F? Are they teachers? Yes.
Do the other two staff members get the cake from Jennings? from the matron? from the headmaster? This.

[doriana_]

Were the two teachers present when the cake was cut?
Relevant what subjects they teach? Are they math teachers?

[GalFisk]

Were the two teachers present when the cake was cut? No.
Relevant what subjects they teach? No. Are they math teachers? One of them teaches math among other subjects, but it's not relevant to the puzzle.

[Sundowner64]

Did Jennings himself decide to stop after quarters? Did someone tell him? Darbishire? other kids?
Did the kids discuss what to do with the cake as it apparently cannot be cut nicely into pieces? did they decide to offer it to the teachers instead?
Did Jennings (or someone else?) go to the matron or the headmaster for help? or did he go to get help but ran into the headmaster?
Did Darbishire blame his granny because the cake was so small? and Jennings blamed geometry because a long roll instead of a flat round piece would have been much easier to cut?

[JenBurdoo1]

Is the "cut it yourself" method of fairly dividing a cake relevant?

[GalFisk]

Did Jennings himself decide to stop after quarters? Did someone tell him? Darbishire? other kids? See below.
Did the kids discuss what to do with the cake as it apparently cannot be cut nicely into pieces? Yes. did they decide to offer it to the teachers instead? No!
Did Jennings (or someone else?) go to the matron or the headmaster for help? or did he go to get help but ran into the headmaster? Jennings went to the Matron for help, while she was talking to the headmaster.
Did Darbishire blame his granny because the cake was so small? Yes, explore. and Jennings blamed geometry because a long roll instead of a flat round piece would have been much easier to cut? If it was the same size, a roll would be hard to divide up as well. Possibly Jennings would've blamed something else then, but it doesn't matter.

Is the "cut it yourself" method of fairly dividing a cake relevant? No.

[doriana_]

Did the grandma mean for the cake to be so small?
Did she bake it with the idea that Darbishire would share the cake with his classmates? Was she mistaken about the number of classmates?

[GalFisk]

Did the grandma mean for the cake to be so small? Yope, explore.
Did she bake it with the idea that Darbishire would share the cake with his classmates? No. Was she mistaken about the number of classmates? Irr.

[doriana_]

Did the grandma make a relevant mistake at any point? E.g., she wanted to make a 10 inch cake but made a 10 cm cake instead?
Relevant how small the cake is exactly?
Had Darbishire asked for the cake? Was the cake made for special occasion, e.g. Darbishire's birthday?

[GalFisk]

Did the grandma make a relevant mistake at any point? Possibly. E.g., she wanted to make a 10 inch cake but made a 10 cm cake instead? No.
Relevant how small the cake is exactly? No.
Had Darbishire asked for the cake? No. Was the cake made for special occasion, e.g. Darbishire's birthday? It's never mentioned.

[Sundowner64]

Did the grandma mean to make the cake for the whole class? for Darbishire only? for Darbishire and his roommates? for the teachers?
Was anyone at the school mistaken about who the cake was intended for?
Was there a deal made between the teachers and the class? like: the teachers get this small cake and provide a big cake to the class in return?

[GalFisk]

Did the grandma mean to make the cake for the whole class? for Darbishire only? This probably, but she normally makes one that's big enough for a whole class anyway. for Darbishire and his roommates? for the teachers?
Was anyone at the school mistaken about who the cake was intended for? Yes.
Was there a deal made between the teachers and the class? No. like: the teachers get this small cake and provide a big cake to the class in return? No, but somewhat OTRT.

[doriana_]

Was Darbishire mistaken about who the cake was intended for? was Jennings? the headmaster? the matron? the classmates? the two other relevant teachers?

[GalFisk]

Was Darbishire mistaken about who the cake was intended for? No. was Jennings? No. the headmaster? Yes, most relevantly. the matron? Yes. the classmates? No. the two other relevant teachers? Yes.

[doriana_]

Did the headmaster, the matron and the teachers think the cake was for them? Relevant what made them think so?

[GalFisk]

Did the headmaster, the matron and the teachers think the cake was for them? Yes. Relevant what made them think so? Yes.

[doriana_]

Did any of them misunderstand something that Jennings said? that Darbishire said? that someone else said?

[GalFisk]

Did any of them misunderstand something that Jennings said? Yes. that Darbishire said? that someone else said? No to both.

[doriana_]

Is this because they only hear part of what Jennings said? because Jennings's wording was ambiguous?
Is what Jennings said related to cutting the cake? the number of pieces? distributing the cake? eating the cake? the cake being small?

[GalFisk]

Is this because they only hear part of what Jennings said? because Jennings's wording was ambiguous? This.
Is what Jennings said related to cutting the cake? the number of pieces? distributing the cake? eating the cake? the cake being small? It's not important. The headmaster sees a small cake cut in 4 reasonable pieces and makes an assumption, which Jennings is too embarrassed to contradict.

[Sundowner64]

So the first part is solved now?
Darbishire's grandma sent a cake to the school and for some reason the cake ended up in Darbishire's class. This meant, the boys had to share it with the whole class. The kids first thought that each of them would get a big slice but after seeing the cake they realized that the slices would be really tiny. Darbishire blamed grandma because the cake was so small, and Jennings blamed geometry because it's hard to cut a cake like this in 36 equal pieces.
Jennings nevertheless attempted but stopped after 4 pieces and went to the matron for help. The headmaster saw the cake cut into four pieces and took it for the teachers. Jennings did not dare to object.
So, the kids saw that they would not get any cake. Darbishire blamed Jennings because he went to the matron. Jennings blamed the headmaster for taking the cake.
Right so far?
Did then Jennings later go to the headmaster/the matron to clear up the situation? Did the matron provide a new cake for the kids?
Did Darbishire decide not to tell the class? and share the cake just with the roommates?

[GalFisk]

So the first part is solved now? Essentially, see below.
Darbishire's grandma sent a cake to the school Yes. and for some reason the cake ended up in Darbishire's class. No. This meant, the boys had to share it with the whole class. No, that was the intention all along, before the cake even arrived. Darbishire was bragging about the cake to everyone, there was a lot of drama with a list of cake recipients and who should be included, but that didn't fit in the puzzle. The kids first thought that each of them would get a big slice Yes. but after seeing the cake they realized that the slices would be really tiny. Yes. Darbishire blamed grandma because the cake was so small, Yes. He thought she'd send one of her huge homemade cakes, but she sent a small store-bought one. and Jennings blamed geometry because it's hard to cut a cake like this in 36 equal pieces. Yes. He thought he was very clever dividing 360 degrees into 36, being that he wasn't normally good at math, but then he saw what it would entail in practice.
Jennings nevertheless attempted but stopped after 4 pieces and went to the matron for help. Correct. The headmaster saw the cake cut into four pieces and took it for the teachers. Yes, he was talking to the matron when Jennings tried to interrupt, and assumed Jennings was treating them to the slices. Jennings did not dare to object. Correct.
So, the kids saw that they would not get any cake. Darbishire blamed Jennings because he went to the matron. Jennings blamed the headmaster for taking the cake. all correct.
Right so far? Yes.
Did then Jennings later go to the headmaster/the matron This. to clear up the situation? Did the matron provide a new cake for the kids? Yes to both.
Did Darbishire decide not to tell the class? and share the cake just with the roommates? Yes to both.

The first part is solved. Darbishire and his roomates will share the replacement cake the matron baked, which, as one of them exclaimed "must be a lot bigger than 360 degrees around!". Only the two last lines of the puzzle statement now remain:
Then, Darbishire thought they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster.
In the end, Darbishire and his roommates got a giant slice of cake each.

[doriana_]

Did Darbishire think there would be no cake at all because of something someone said? something someone did? Did he think that there would be no replacement cake at all? That someone else would take/eat the replacement cake?
When Darbishire thought there would be no cake, had the replacement cake already been promised? baked?
Relevant why the replacement cake is only for the roommates and not for the whole class?
Relevant who cut the replacement cake? If so, the matron? Jennings? Darbishire?

[GalFisk]

Did Darbishire think there would be no cake at all because of something someone said? No. something someone did? Yes. Did he think that there would be no replacement cake at all? Incorrect. That someone else would take/eat the replacement cake? No, but...
When Darbishire thought there would be no cake, had the replacement cake already been promised? baked? Yes.
Relevant why the replacement cake is only for the roommates and not for the whole class? No, that's just an idea the roommates came up with.
Relevant who cut the replacement cake? No. If so, the matron? Jennings? Darbishire?

[doriana_]

Did Darbishire think there would be no cake at all because of something Jennings did? Something the matron did? Something the headmaster did?
When he thought there would be no cake, had he already seen the replacement cake?
Did someone drop the replacement cake or otherwise ruin it?

[GalFisk]

Did Darbishire think there would be no cake at all because of something Jennings did? Yes. Something the matron did? No. Something the headmaster did? Yes.
When he thought there would be no cake, had he already seen the replacement cake? Yes.
Did someone drop the replacement cake Darbishire thought so.or otherwise ruin it?

[doriana_]

Did Jennings and the headmaster crash into each other? If so, did either of them drop anything? And Darbishire thought it was the cake? Or did either of them indeed drop the cake but managed to catch it in time?

[GalFisk]

Did Jennings and the headmaster crash into each other? No. If so, did either of them drop anything? So no - but see next. And Darbishire thought it was the cake? Yes. Or did either of them indeed drop the cake but managed to catch it in time? No.

[Sundowner64]

Did Darbishire think someone dropped the cake? Jennings? the headmaster?
But actually noone dropped anything?
Did Darbishire see/hear something relevant?
Did the headmaster bring the cake to Darbishire and his roommates? Jennings? the matron? someone else?
Did Jennings play a prank on Darbishire?

[GalFisk]

Did Darbishire think someone dropped the cake? Yes. Jennings? the headmaster? This. But he blamed Jennings.
But actually noone dropped anything? No, someone dropped something.
Did Darbishire see/hear something relevant? Yes, hear.
Did the headmaster bring the cake to Darbishire and his roommates? Jennings? the matron? This. someone else?
Did Jennings play a prank on Darbishire? Yes.

[Sundowner64]

So Darbishire thanked Jennings for clearing up the situation and Jennings thanked the matron for a new cake.
Then Jennings let it sound as if someone had dropped the cake in order to prank Darbishire.
Darbishire blamed Jennings for having dropped the cake and Jennings blamed the headmaster.
But the cake was still there and Darbishire and his roommates could enjoy a big slice each.
What else needs to be found out?

[GalFisk]

So Darbishire thanked Jennings for clearing up the situation and Jennings thanked the matron for a new cake. Correct.
Then Jennings let it sound as if someone had dropped the cake in order to prank Darbishire. No, but OTRT.
Darbishire blamed Jennings for having dropped the cake and Jennings blamed the headmaster. Not exactly, explore.
But the cake was still there and Darbishire and his roommates could enjoy a big slice each.Yes.
What else needs to be found out? See above. There's a whole sequence of events to be discovered.

[doriana_]

Relevant why Jennings played a prank on Darbishire?
Did the prank involve Jennings dropping something? someone else dropping something?
Did Jennings exclaim something like "Oh no, the cake!"?

[GalFisk]

Relevant why Jennings played a prank on Darbishire? No, it was a spur of the moment thing.
Did the prank involve Jennings dropping something? No. someone else dropping something? No, but...
Did Jennings exclaim something like "Oh no, the cake!"? No!

[doriana_]

Did Jennings relevantly exclaim anything? Did anyone else?

[GalFisk]

Did Jennings relevantly exclaim anything? Did anyone else?Everyone present said things, but "exclaim" is probably not the right word.

[GalFisk]

Hint: someone is doing something underhanded, apart from Jennings pranking Darbishire.

[Sundowner64]

Someone: Jennins? Darbishire? the headmaster? the matron? someone else?

[GalFisk]

Someone: Jennins? Darbishire? Yes to both. the headmaster? No. the matron? Yesish. someone else? Yes, the other roommate of Jennings and Darbishire, named Atkinson. Not that relevant though, the puzzle would work without him.

[Sundowner64]

Does Jennings' prank on Darbishire basically mean that Jennings makes Darbishire believe the cake is destroyed?
Is the underhanded thing related to the cake at all?
Is it initiated by the matron? is it something good? bad? a surprise?
Is it done to circumvent the headmaster in some way?

[GalFisk]

Does Jennings' prank on Darbishire basically mean that Jennings makes Darbishire believe the cake is destroyed?This is not the intention.
Is the underhanded thing related to the cake at all? Yes.
Is it initiated by the matron? This. is it something good? bad? Depends on whose perspective it's seen from.a surprise? No.
Is it done to circumvent the headmaster in some way? Yes.

[Sundowner64]

Did the matron want to give the cake to the kids without the headmaster knowing it?
Was the cake in a box? was it disguised as something else?
Did the matron bring the cake to the kids? did Jennings? Darbishire? someone else?
Did Jennings' prank happen on the way from the matron to the kids' room? in the kids' room? indoors? outdoors? was the headmaster present?

[GalFisk]

Did the matron want to give the cake to the kids without the headmaster knowing it? Yes.
Was the cake in a box? Assume yes. was it disguised as something else? No.
Did the matron bring the cake to the kids? Yes. did Jennings? Darbishire? someone else?
Did Jennings' prank happen on the way from the matron to the kids' room? in the kids' room? This. indoors? outdoors? But also this. was the headmaster present? Eventually.

[Sundowner64]

Can we have a recap, please? and what we still need to find out?
Thanks.

[GalFisk]

Can we have a recap, please? and what we still need to find out?
Thanks.

Sure thing.

First, Darbishire told Jennings and all his other classmates at the Linbury Court boarding school that they would be getting a big slice of cake each.
Because Darbishire's grandma had written that she'd be sending a cake, and she was known for sending big cakes.

Then, the classmates saw that they'd only be getting a tiny sliver of cake each. Darbishire blamed his grandma for this, and Jennings blamed geometry.
Because grandma only sent a small store-bought cake, after Darbishire had already promised everyone a slice. Jennings helpfully figured outt hat slicing it into 10° slices would do it, but that meant the slices would be tiny.

Then, they saw that they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster.
Because Jennings. after slicing the cake in four, wanted to ask the matron for help with making the small slices with her big sharp knife, and the headmaster misunderstood his flustered questions as him wanting to give the cake to the matron, himself and two teachers, and he was too flabbergasted to protest.

Then, Darbishire and his roommates thought they'd be getting a giant slice of cake each. Darbishire thanked Jennings for this, and Jennings thanked the matron.
After some commotion, Jennings came clean to the matron, who promised to bake a new cake and sneak it to the boys if they went to bed early that day. The boys decided not to share this new cake with the other classmates, since they didn't expect there to be any cake.

Then, Darbishire thought they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster.
The matron brought the cake to the dorm room. You need to find out what happened afterwards. Jennings' prank leads Darbishire to think that the headmaster caused the cake to drop, and that it was Jennings' fault. In reality, something else dropped. The outdoors is relevant.

In the end, Darbishire and his roommates got a giant slice of cake each.
The undiscovered antics above eventually led to a successful conclusion.

[Sundowner64]

Did the headmaster drop something? the matron? Jennings? Darbishire? someone else? indoors? outdoors? on purpose?
Was someone outdoors? the headmaster? was there a relevant sound/noise/call outside?
Did the headmaster show up on the scene? before the cake was delivered? during? after?
Did someone call the headmaster? did he appear just by chance? did he hear/smell/notice something?
Did Jennings' prank involve that he said something? to Darbishire?

[GalFisk]

Did the headmaster drop something? Indirectly, yes. the matron? Jennings? Darbishire? someone else? indoors? outdoors? This. on purpose? No.
Was someone outdoors? the headmaster? No to both. was there a relevant sound/noise/call outside? Yes.
Did the headmaster show up on the scene? before the cake was delivered? during? after? Yes, this.
Did someone call the headmaster? No. did he appear just by chance? No, explore. did he hear/smell/notice something? No.
Did Jennings' prank involve that he said something? to Darbishire? No to both.

[Sundowner64]

Was the headmaster outdoors when something dropped? indoors? did he do something indoors that made something outdoors drop? or make the sound as if something would drop? did he throw something out of the window?
Did the sound from outside come from a person? an animal? a natural thing? a manmade thing? was there a relevant damage?
Did someone go outside to check what happened? the headmaster? the matron? Jennings? Darbishire?
Was the cake already in Jennings' room when the noise came from outside? Was the cake in a closed box? relevant?

[GalFisk]

Was the headmaster outdoors when something dropped? indoors? This. did he do something indoors that made something outdoors drop? Yes. or make the sound as if something would drop? No.did he throw something out of the window? No, but...
Did the sound from outside come from a person? an animal? a natural thing? a manmade thing? This. was there a relevant damage? No.
Did someone go outside to check what happened? the headmaster? the matron? Jennings? Darbishire? No to all.
Was the cake already in Jennings' room when the noise came from outside? Yes. Was the cake in a closed box? Assume yes. relevant? Not really.

[Sundowner64]

Did someone outside drop the thing? if so: in reaction to something the headmaster said or did? Did the headmaster call or shout at the window?
If the cake box was closed: did the kids know that there is a cake in it? did they first think the box might be empty? that the whole thing is a prank?

[GalFisk]

Did someone outside drop the thing? No. if so: in reaction to something the headmaster said or did? So no. Did the headmaster call or shout at the window? No, but...
If the cake box was closed: did the kids know that there is a cake in it? Yes, they got to see it. did they first think the box might be empty? that the whole thing is a prank? No to both.

[Sundowner64]

Did something outdoors drop from the roof? from the window or other parts of the house? from a tree?
Did the headmaster simply open the window?
Was the headmaster's action and its consequence part of the prank? Did the headmaster know of the prank? was he the prankster?

[GalFisk]

Did something outdoors drop from the roof? from the window or other parts of the house? This. from a tree?
Did the headmaster simply open the window? Yes.
Was the headmaster's action and its consequence part of the prank? No. Did the headmaster know of the prank? was he the prankster? No to both.

[Sundowner64]

Did he drop the window? parts of it? something that was standing on the window sill?
Did he cause an icicle to drop?
Relevant why the headmaster opened the window?
Did the headmaster notice that something dropped?
Did he go down to see what happened? and thus, passed by the kids room and saw the cake?

[GalFisk]

Did he drop the window? parts of it? No to both. something that was standing on the window sill? No, but explore.
Did he cause an icicle to drop? No.
Relevant why the headmaster opened the window? Just to let in some air.
Did the headmaster notice that something dropped? Yope - he suspected it but the boys convinced him that it was nothing.
Did he go down to see what happened? and thus, passed by the kids room and saw the cake? No to both. Potential FA.

[Sundowner64]

Was Darbishire the intended victim of Jennings' prank? the headmaster? the matron? fellow students? someone else?
Did the prank involve make the headmaster open the window? Did Jennings place something at or around the window that would necessarily drop when the windows is opened? or give the impression that something dropped? Was the idea to make the headmaster look out of the window?
Were the boys present when the headmaster opened the window? did this happen in the boys' dorm room? Was the cake on the table at that moment? in the closed box?
Did Darbishire think the cake was hidden outside on the window sill and dropped when the headmaster opened the window?

[GalFisk]

Was Darbishire the intended victim of Jennings' prank? Yes. the headmaster? the matron? fellow students? someone else? No to the rest.
Did the prank involve make the headmaster open the window? No. Did Jennings place something at or around the window that would necessarily drop when the windows is opened? Yesish.or give the impression that something dropped? Was the idea to make the headmaster look out of the window? No.
Were the boys present when the headmaster opened the window? did this happen in the boys' dorm room? Yes to both. Was the cake on the table at that moment? No. in the closed box? Yes.
Did Darbishire think the cake was hidden outside on the window sill and dropped when the headmaster opened the window? Yes!

The rest is details, so here's the
SPOILER

First, Darbishire told Jennings and all his other classmates at the Linbury Court boarding school that they would be getting a big slice of cake each - because his grandma had written to tell him that she'd be senging a cake in a package, and she was well-known for baking giant, fantastic cakes.
Then, the classmates saw that they'd only be getting a tiny sliver of cake each. Darbishire blamed his grandma for this, and Jennings blamed geometry. - Grandma hadn't had time to bake a cake, nad had bought one in a pastry shop. Jennings realized that they could geometrically divice a 360 degree cake into 36 slices of 10 degrees each, butlater realized that those slices would be mere slivers. They cut it in four, then Jennings went to ask Matron if she could use her big sharp knife to cut it.
Then, they saw that they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster - the headmaster thought that Jennings was giving the cake to Matron, him and the two teachers for their class.
Then, Darbishire and his roommates thought they'd be getting a giant slice of cake each. Darbishire thanked Jennings for this, and Jennings thanked the matron - when Matron heard about the story, after the subsequent fight that got Jennings sent from the table, she promised to bake them a new cake. She would take it to their dorm before bedtime, if they promised to be there in time.
Then, Darbishire thought they'd be getting no cake at all. Darbishire blamed Jennings for this, but Jennings blamed the headmaster - they had to hide the cake, so thet the headmaster wouldn't find it during the inspection during bedtime, and decided to hang it outside the window in a gym bag, leaving just a bit of string on the inside. At the last minute, while Darbishire was washing up, jennings and the other roommate decided to swap the cake for a pair of gym shoes as a prank.
In the end, Darbishire and his roommates got a giant slice of cake each - The headmaster opened the window in order to let in some fresh air (which was partially Darbishire's fault, as he, in his bumbling attempts at pretending like nothing was up, started rambling on aboutb the weather), but fortunately only dropped the old gym shoes, and not the cake which had been hidden under a bed.