### Brain Teasers

# 4 X 4

Math
Math brain teasers require computations to solve.

Below there are sixteen numbers. Assuming that any three of the numbers may be drawn at random, what are the chances that three numbers will be drawn whose sum equals six?

1 2 3 1

2 3 1 2

3 1 2 3

1 2 3 1

1 2 3 1

2 3 1 2

3 1 2 3

1 2 3 1

### Answer

This is a bit tricky and I initially thought the answer was 1/16 or 6.2% but it is really 2/7 or 28.6%.Either drawing '2 2 2' or some combination of '1 2 3' adds up to be 6. The chances of getting '2 2 2' are 5/16 (5 2s out of 16) times 4/15 (4 2s left out of 15) times 3/14 (3 2s left out of 14). This is 5/16 * 4/15 * 3/14 which equals 1/56.

The chances of getting some combination of '1 2 3' is equal to 6/16 (6 1s in the list) times 5/15 (5 2s out of 15 numbers left) times 5/14 (5 3s out of 14 numbers left) times the number of different combinations of '1 2 3' which is 6. This is 6/16 * 5/15 * 5/14 * 6 which equals 15/56.

1/56 + 15/56 = 16/56 or 2/7 or ~28.6%.

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