A candy company puts 3 gumdrops in each bag. How many gumdrops will the company need to fill 5,000 bags?
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Consider the 50 odd numbers 1,3, 5, ..., 99.
For each one, form a box containing the number and all powers of 2 times
the number.
So the first box contains {1,2,4,8, 16,..}
the next box contains {3,6,12,24,48, ...}
Then among the 51 numbers chosen, the pigeonhole principle tells us that there are two that are contained in the same box. They must be of the form and
with the same odd number k. So one will divide the other.
According to the pigeonhole principle, if n items are placed in m containers, with n > m, at least one container must contain more than one item.
For example, if you have three gloves (and none of them are ambidextrous/reversible), you must have at least two right-handed gloves or at least two left-handed gloves, because there are three objects but only two categories of handedness to put them into.
To learn more about pigeonhole principle from the given link
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