joynal2u wrote:
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 ?
A. Three
B. Four
C. Five
D. Six
E. Seven
Amazing question | Sharing the method to solve backwards from answer optionsOption A - Say we pick up (0, 1, 2) or (3, 4, 5) then we do not get a 10 whereas if we pick up (
4, 5,
6) or (0,
1,
9) then we get a sum of 10 from two slips
Option B - Say we pick up (0, 1, 2, 3) or (2, 3, 4, 5) then we do not get a 10 whereas if we pick up (3,
4, 5,
6) or (0,
1, 2,
9) then we get a sum of 10 from two slips
Option C - Say we pick up (0, 1, 2, 3, 4) or (1, 2, 3, 4, 5) then we do not get a 10 whereas if we pick up (2, 3,
4, 5,
6) or (0,
1, 2, 3,
9) then we get a sum of 10 from two slips
Option D - Say we pick up (0, 1, 2, 3, 4, 5) then we do not get a 10 whereas if we pick up (1, 2, 3,
4, 5,
6) or (0, 1,
2, 3, 4,
8) then we get a sum of 10 from two slips
Option E - Say we pick up (0, 1, 2, 3,
4, 5,
6) or (1, 2,
3,
4, 5,
6,
7) or (
4, 5,
6, 7, 8, 9, 0) or
any other combination of 7 integers between 0 and 9, incl. we will get at least 1 pair of integers that sums to 10
Ans.
E