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# Apples and Monkeys

31 replies to this topic

### #1 babbal

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Posted 02 October 2007 - 01:36 AM

There are 5 Monkeys and a number of apples. They want to divide the apples into equal shares, but all forget. They all go to sleep. In the middle of the night, the first monkey suddenly remembers, and goes and divides the apples into five equal groups. He finds out that there is an extra, and eats it. Then, he hides his share and goes to sleep. The second monkey remembers ten minutes later, divides the apples, and finds out there is an extra. He eats the extra, hides his share and goes to sleep. The third, fourth, and fifth all do the same process, and at the end, there are still many apples left. Assuming that the monkeys didn't cut any apples, what is the least number of apples that there could've been at the beginning?
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### #2 Writersblock

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Posted 02 October 2007 - 07:25 AM

3121. Monkey 1 sees them and divides them into 5 shares of 624. He hides his share and eats the left over. Monkey 2 sees the 4 shares of 624 and divides them into 5 shares of 499. He eats 1 and hides his 499. Monkey 3 sees the 4 shares of 499. He divides them into 5 shares of 399 and eats 1. He hides his 399. Monkey 4 sees the 4 shares of 399. He divides them into 5 shares of 319 and eats 1. He hides his 319. Monkey 5 sees the 4 shares of 319. He divides them into 5 shares of 255. He eats the left over and hides his 255. There are 1020 left over.
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### #3 Ploper

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Posted 02 October 2007 - 11:59 PM

duuude.

That's a lot of apples
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### #4 Writersblock

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Posted 03 October 2007 - 04:10 AM

Anyone find a lower one that divides into whole apples?
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### #5 bonanova

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Posted 03 October 2007 - 06:03 AM

Anyone find a lower one that divides into whole apples?

After a little math, you can show that the final share has to be 1 less than a power of 2.
A simple program to calculate the other shares does not give integral values for 15, 31, 63 or 127,
but does for 255: -> 255 319 399 499 624 ---> 3121.
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Vidi vici veni.

### #6 ssxm

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Posted 28 February 2008 - 06:30 PM

how could you forget about 3121 apples laying in front of your face i know their monkeys but please 3121 APPLES !! how could you !!!!
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### #7 mohamdy

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Posted 28 February 2008 - 10:10 PM

The Number is 31 apples
MONKEY 1 sees 31 apples he eats 1 and distribute 30 into 5 groups of 6 apples hides his 6 apples and leave 24 apples
MONKEY 2 sees 24 apples he eats 4 and distribute 20 into 5 groups of 4 apples hides his 4 apples and leave 16 apples
MONKEY 3 sees 16 apples he eats 1 and distribute 15 into 5 groups of 3 apples hides his 3 apples and leave 12 apples
MONKEY 2 sees 12 apples he eats 2 and distribute 10 into 5 groups of 2 apples hides his 2 apples and leave 10 apples
MONKEY 1 sees 8 apples he eats 3 and distribute 5 into 5 groups pf 1 apple hides his 1 apple and leave 4 apples

I first thought of 26 but mokey 2 would have 20 apples which will be distributed and he would not have any apple to eat

Edited by mohamdy, 28 February 2008 - 10:11 PM.

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Posted 28 February 2008 - 10:23 PM

For the second monkey you have taken away 4 then taken another 4 away so atotal of 8 overall;
He ate 4 then hid 4.

MONKEY 2 sees 24 apples he eats 4 and distribute 20 into 5 groups of 4 apples hides his 4 apples and leave 16 apples

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### #9 storm

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Posted 29 February 2008 - 09:50 AM

The Number is 31 apples
MONKEY 1 sees 31 apples he eats 1 and distribute 30 into 5 groups of 6 apples hides his 6 apples and leave 24 apples
MONKEY 2 sees 24 apples he eats 4 and distribute 20 into 5 groups of 4 apples hides his 4 apples and leave 16 apples
MONKEY 3 sees 16 apples he eats 1 and distribute 15 into 5 groups of 3 apples hides his 3 apples and leave 12 apples
MONKEY 2 sees 12 apples he eats 2 and distribute 10 into 5 groups of 2 apples hides his 2 apples and leave 10 apples
MONKEY 1 sees 8 apples he eats 3 and distribute 5 into 5 groups pf 1 apple hides his 1 apple and leave 4 apples

I first thought of 26 but mokey 2 would have 20 apples which will be distributed and he would not have any apple to eat

Each monkey ate 1 apple while dividing...you are wrong!!
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### #10 mohamdy

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Posted 03 March 2008 - 08:45 AM

In the puzzle
He Says He finds out that there is an extra, and eats it

he did not say there is 1 extra .
i think here that "there is an extra" means that the extra number is unknown
and "eats it" means he eats this extra
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