### Brain Teasers

# Twos and Fives

We have 10 2's and 10 5's. Pick some of them, and add them together. If we pick them all, we get the sum 70. Which sums between 1 and 70 are impossible?

### Hint

1 and 3 are impossible.### Answer

By symmetry, 67 and 69 are also impossible. Other sums can be constructed easily.Therefore, four sums 1, 3, 67 and 69 are impossible.

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