Simple Sum

Which number must be written in the place of the dots?

Remark: The missing number does not necessarily have 3 digits.

If you turn the paper around, the text will read:

… = 19969 + 68199
99106 = 18108 + 80998

Therefore, the missing number is 88168, which after 180 degrees rotation becomes 89188.

Game of NIM

Two people play a game of NIM. There are 100 matches on a table, and the players take turns picking 1 to 5 sticks at a time. The person who takes the last stick wins the game. Who has a winning strategy?

The first person has a winning strategy. First, he takes 4 sticks. Then every time the second player takes X sticks, the first player takes 6 – X sticks.

Halloween Candies

A mother has 4 children. On Halloween, she decides to give them 200 candies one by one, starting with the youngest child, then the second youngest, third youngest, etc. At some point, they have to interrupt the procedure and eat dinner, but when they continue, nobody remembers which was the last child to get a candy. How can the mother distribute the remaining candies to the kids without starting over again or counting how many candies have been given so far?

The mother can start giving the remaining candies one by one in the reverse order, starting with the oldest child, then the second oldest, etc.