There are 100 monkeys in a zoo and they feed them 1600 bananas.
Can you show that at least 4 monkeys get the same number of bananas, no matter how the monkeys distribute them among each other?
via DerSpiegel
6 comments:
Lee
said...
Assume it can be done in groups of 3. So 3 monkeys get 0 bananas 3 get 1 banana, etc up to 3 get 32 bananas which leaves one monkey to get 33 bananas. But the total number of bananas needed then becomes 1617 bananas which is more than the total number of bananas available. So it is impossible in groups of 3 monkeys. At least one group of 4 monkeys gets the same number of bananas, but that group of 4 monkeys must get 17 or fewer bananas a piece in order for the total number of bananas to total tp 1600.
Exactly. Just one minor correction; in my calculation the first 99 monkeys get 1584 bananas, this leaves us with 16 so the group with 4 monkeys would get 16 bananas (or less).
>> so the group with 4 monkeys would get 16 bananas (or less).
Yeah, that's right. I won't try to explain precisely why I said 17 except to say it had nothing to do with the number 617. It had to do with group number being one less than banana number in the way I set it up (because group 1 gets zero bananas) and me reading the group number column instead of banana number column.
I just returned two days ago. Irma is still far away and should become an issue for us after Wed. Until then my preparation(s) are limited to checking the NHC webpage once a day.
6 comments:
Assume it can be done in groups of 3. So 3 monkeys get 0 bananas 3 get 1 banana, etc up to 3 get 32 bananas which leaves one monkey to get 33 bananas. But the total number of bananas needed then becomes 1617 bananas which is more than the total number of bananas available. So it is impossible in groups of 3 monkeys. At least one group of 4 monkeys gets the same number of bananas, but that group of 4 monkeys must get 17 or fewer bananas a piece in order for the total number of bananas to total tp 1600.
Exactly.
Just one minor correction; in my calculation the first 99 monkeys get 1584 bananas, this leaves us with 16 so the group with 4 monkeys would get 16 bananas (or less).
>> so the group with 4 monkeys would get 16 bananas (or less).
Yeah, that's right. I won't try to explain precisely why I said 17 except to say it had nothing to do with the number 617. It had to do with group number being one less than banana number in the way I set it up (because group 1 gets zero bananas) and me reading the group number column instead of banana number column.
>> nothing to do with the number 617
That should read 1617. For lack of a better explanation, I guess I'll claim old age for all of my mistakes.
If your are still in the Bahamas, I trust you are battening the hatches.
CIP,
I just returned two days ago.
Irma is still far away and should become an issue for us after Wed.
Until then my preparation(s) are limited to checking the NHC webpage
once a day.
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