### Brain Teasers

# Pick-up Sticks

You and your friend, who is always tricking you, are playing a game of pick-up sticks when he/she decides to change the rules.

The object of the game is to make the other player pick up the last stick. You can only pick up either 1,2,or 3 sticks on your turn. One player chooses how many sticks will be in the pile and the other goes first.

This time you go first and your friend chooses 29 sticks. Are you going to win? What is the strategy your friend uses?

The object of the game is to make the other player pick up the last stick. You can only pick up either 1,2,or 3 sticks on your turn. One player chooses how many sticks will be in the pile and the other goes first.

This time you go first and your friend chooses 29 sticks. Are you going to win? What is the strategy your friend uses?

### Hint

Your friend is very smart.### Answer

No, you are not going to win if your friend knows the correct strategy. Whatever number of sticks that you pick on each turn, your friend will subtract that number from four and pick that many sticks:You pick 1, he picks 3

You pick 2, he picks 2

You pick 3, he picks 1

Then the total number of sticks will have to be one more than a number divisible by four. This will guarantee that there is one stick left after his last turn.

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