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Each of the integers from 0 to 9, inclusive, is written on a

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New post 25 Jun 2007, 15:00
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21. Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
3
4
5
6
7 *
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New post 25 Jun 2007, 15:17
There are 4 pairs of the numbers with sum 10.

{ {1,9}, {2,8}, {3,7}, {4,6}}

now lets consider the worst case. so we pick the 2 left out numbers first - 0 and 5.

then we pick a next number from the one of the pairs above. now to continue and not to make the sum of 10, we need to pick a number from the left out pairs. This process can be repeated till no pair is left out, which is 4. so we can pick 6 numbers without making the sum 10.

e.g. 0, 5, 1, 8, 7, 4

but any number that you pick next would give us the sum 10 with it's paired number.

So the answer is 7.
  [#permalink] 25 Jun 2007, 15:17
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Each of the integers from 0 to 9, inclusive, is written on a

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