So I am back in the surface! [Part IV]
All industrial food items in the Underground, the one made by companies for monster consumption, have some weird qualities. First off, they can't be divided or cut for the intent of sharing , if the food item is meant to be eaten alone. This includes Glamburgers , Monster Candy, and Astronaut Food. Secondly, they can only be consumed , no other things can be done by them, you can't even bite down to cut them to two, they will disappear .
Now, into the question, Alphys decides to buy a whole tray of Glamburgers, I mean, a whole tray. The thing is, we will never know how large the tray is. All we know is it is a perfect square that is gridded (grid is also made up of perfect squares) that each contain a Glamburger, like the picture below.
Alphys divides this among three people: herself, Papyrus, and Undyne, but she said that any extra Glamburgers that remain in the tray after proper division are for her, usually not her behavior.
The question is, how many Glamburgers in maximum could end up as extras
after the initial division (consider all scenarios)
Remember, they can’t be divided, so no half Glamburgers
I will be impressed if you will post a proof as well :)
Whoever wants to submit a report for this problem can go here
The answer is 1.
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1 solution
I believe this proof, as the guy who got the extra Glamburger by luck was me :)
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@Percy Jackson , I followed your advice this time. Thnx for giving the idea :)
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Glad that you didn't waste a perfectly good solution space lol
A Glamorous burger? Wow...just, wow...
You're a guy!?..
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Ding, ding ding, we have a winner!!! Congrats @Nirjhar Kheto , you're the first (apart from me) to find out that Frisk is not actually a guy, and is pretty stupid for a girl! Your prize is...nothing! I'm so generous, aren't I :P
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@Frisk Dreemurr – Well, don't deny it, you are pretty stupid lmao
What made you think that ftlog?
In the problem description, you mention that the boxes come in perfect cubes, meaning that possible Glamburger amounts could be 1 Glamburger, 8 Glamburgers, 27 Glamburgers, etc. Unless there was a typo in the problem description, since the only possible remainders after perfect division by 3 are 0, 1, or 2, and 5 3 = 1 2 5 Glamburgers divides with 2 as remainder, shouldn't the maximum number of extra Glamburgers be 2, not 1?
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yeah i agree. even 8 is 3k+2.
maybe the box was meant to be a square box. but the wording says cube.
anyway it's a nice idea.
i don't get why Monster Candy and Astronaut Food are mention in the description.
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I am very sorry @Alexander McDowell and @num IC , the question is now corrected. Feel free to report my other questions once you find a flaw in them in the report room (link in question itself)
Monster Candy and Astronaut Food are other great fooditems you can find in the depths of the Underground. They are quite famous as well among monsters
If you were wondering, these are references to Undertale
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@Frisk Dreemurr – "In case you're wondering..."
Nobody will wonder Dreemurr, they know you too well to think you won't try choking people with Undertale references (lol)
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@A Former Brilliant Member – lmfao, at least I don't brag about how great I am in my monologue (lel)
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@Frisk Dreemurr – At least I brag about things that are worth bragging about 😎
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@A Former Brilliant Member – Bragging that you "only brag things that are worthful" isn't worthful Percy...
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@Frisk Dreemurr – I would argue, but its no use talking to someone who has a lump of pixels in their head instead of an actual brain. Ciao!
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I would argue, but its no use talking to someone who has a lump of pixels in their head instead of an actual brain. Ciao!
This is the formal way of saying
"I can't waste time for your petty comebacks girl lmao XD lol lmfao"
...lol
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@Frisk Dreemurr – lol technically :P
@Frisk Dreemurr I've beaten Undertale all endings and still don't know what a Glamburger look like.
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The pic is strictly canon, you can see it in the menu of the MTT-Brand Burger Emporium while buying food from Burgerpants
Look at the the top left corner of Burgerpants' store, all the four items buyable are depicted there
The image link to MTT-Brand Burger Emporium
Every positive integer is of one of the three forms:
3 k , 3 k + 1 , or 3 k + 2 for some k
So we consider the square of each in turn.
( 3 k + 1 ) ² = 9 k ² + 6 k + 1 ; m = 3 k ² + 2 k
( 3 k + 1 ) ² = 3 m + 1