How many Donuts?

Question

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

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.
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.
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.
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.

this is my first time on puzzling and first question. so I dont know the tradition here — Arun Karnawat, Jan 09 '18 at 07:58
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 09 '18 at 07:59
This is a nice problem. However, the site consensus has voted that math textbook type problems are off-topic here. — Bass, Jan 09 '18 at 08:28
That is an onigiri, not a tent! :P But good creative way of using emojis. — Ander Biguri, Jan 09 '18 at 09:32
@AnderBiguri what can I say, I did not find emoji for tent, and It look like a tent — Arun Karnawat, Jan 09 '18 at 09:34
@AnderBiguri Are you trying to suggest you don't make your tents out of rice and seaweed?! — , Jan 09 '18 at 13:56
If only there were four of them instead of three, and they had bananas instead of donuts! — shoover, Jan 09 '18 at 15:10
It's not clear if the donut that someone gives to the monkey comes from his own share or it's a remainder of the division in 3 equal shares. (Not sure if this lack of information is part of the puzzle tho') — Dek Dekku, Jan 09 '18 at 16:39

score 8 · Accepted Answer · answered Jan 09 '18 at 08:14

The answer is

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.

Alix Eisenhardt · Answer 2 · 2018-01-09T15:18:30.420

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

Let's start with equations

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.

How many Donuts?

2 Answers2