### Brain Teasers

# Flip 100 Coins

Math
Math brain teasers require computations to solve.

Tom has 100 coins on the table with their heads up. Each time he flips 93 coins, turning heads to tails or vice versa.

What is the least number of times he must do this in order to get all of them tails up?

What is the least number of times he must do this in order to get all of them tails up?

### Hint

Maybe you have seen the "flip 7 in 10" problem and think this one is also 4, but it isn't, because the logic is a little different.### Answer

If you have seen the "flip 9 in 10" problem, you know that you have to leave one coin unflipped each time, and it will require 10 times.In this problem, the first time leaves 7 coins heads up, the second time leaves at most 14 coins TAILS up, the third time leaves at most 21 coins HEADS up, the fourth time leaves at most 28 coins TAILS up, ..., and the fourteenth time leaves at most 98 coins tails up.

The fifteenth time, he flips 1 of the 2 coins that is heads up, and 92 of the coins that are tails up, leaving 93 coins heads up.

The sixteenth and last time he can get all of them tails up.

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