How many Donuts? [closed]

Three friends went on a camping trip and on the way they bought N donuts 🍩. They put them in their tent 🎪, and went swimming 🏊.

1. One of them came and divided the donuts in to 3 equal parts, fed one donut to the monkey, ate his share, then went back to swim.

2. The second friend came along and again he divided the donuts in to 3 equal parts, he fed one donut to the monkey, ate his share and went back to swim.

3. The third friend came along and again he divided the donuts in to 3 equal parts, he fed one donut to the monkey, ate his share and went back to swim.

4. Finally, all of the friends came together, divided the donuts in 3 equal parts and fed one to the monkey, each ate their share and then went home.

How many donuts 🍩 were there in total? What is the value of N?

Hint 1

"N" is an integer

Hint 2

"N" in 2 digit number

Hint 3

Try reverse hit and trial approach.

closed as off-topic by Bass, JMP, user58, Alconja, Beastly GerbilJan 9 '18 at 16:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Bass, JMP, user58, Alconja, Beastly Gerbil
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• hints after 4 miuntes? really? – Marius Jan 9 '18 at 7:55
• ok. fair enough. You have to wait a few hours first. if you don't get an answer add hints, but one at a time. – Marius Jan 9 '18 at 7:59
• That is an onigiri, not a tent! :P But good creative way of using emojis. – Ander Biguri Jan 9 '18 at 9:32
• @AnderBiguri what can I say, I did not find emoji for tent, and It look like a tent – Arun Karnawat Jan 9 '18 at 9:34
• @AnderBiguri Are you trying to suggest you don't make your tents out of rice and seaweed?! – Bilkokuya Jan 9 '18 at 13:56

N = 79

I solved this by tracing from the end towards the start. I couldn't write the solution fully as I'm using my mobile now. But the idea is this:

Denote K as the donuts taken by all friends in the end.

- On scenario 4, there must be 3K + 1 donuts.
- On scenario 3, there must be 9K/2 + 5/2 donuts.
- On scenario 2, there must be 27K/4 + 19/4 donuts.
- On scenario 1 (at the beginning), there must be 81K/8 + 65/8 donuts.

Which is equal to N = 10K + 8 + (K+1)/8 donuts.
To make it an integer, we can pick K = 7 making a final N = 79.

Note that on each scenarios (from 3 to 1) we multiply the previous scenario with 3/2 then plus 1.

I had the same result as @athin but with a different approach.

1. There are 3x + 1 donuts
2. There are 3y + 1 = 2x (remaining of the first scenario) donuts
3. There are 3z + 1 = 2y (remaining of the second scenario) donuts
4. There are 3a + 1 = 2z (remaining third scenario) donuts

So for scenarios 2 to 4, the number of donuts must be even.

From there I tried different values of a.
I suspected that the number was not going to be very big considering the few iterations.
(1. to 4. will be the equations of the corresponding scenarios)

The simplest : a = 1

4. = 4
3. = 7
So it's not 1.

The next one : a = 2

4. = 7
This gives us an odd number immediately, so it's not 2.

And so on :

a = 3

4. = 10
3. = 16
2. = 25

a = 4

4. = 13
Odd result

a = 5

4. = 16
(We stop directly because of the result of a = 3)

a = 6

4. = 19
Odd result

a = 7

4. = 22
3. = 34
2. = 52
We have our three even results so 1. = N = 79 donuts

And I just wanted to add, thanks to the discovery of the total number of donut, that we can find that the final distribution of these was:

33 donuts for the first
24 for the second
18 for the third
and 4 for the monkey

So the moral is: get out of the water before others. If you like donuts. Otherwise be a monkey.