# 4.8.2 Having Fun with Math—the Party Puzzle

The next activity is a number puzzle, which introduces some more ways of adding numbers quickly in your head. You will see how to turn it into a party trick to amuse your friends.

## Activity: Party Puzzle

Write down the numbers 1 to 25 in order, in a 5×5 grid, so that the first row reads 1, 2, 3, 4, 5; the next row begins with 6, and so on.

Now choose five numbers from the grid as follows:

• For the first number, choose any number from the grid. In our example below, we chose 17.
• Now cross out the numbers in the same row and column as the chosen number.
• Choose the second number from the remaining numbers on the grid—our choice is 24. Then, cross out the numbers in the same row and column as the second number.
• Continue in this way until you have chosen five numbers. For example, let’s choose 17, 24, 15, 6, and 3. For your fifth number, there will be only one number left that’s not crossed out.

Try the puzzle at least three more times, choosing different numbers each time. Work out the sums on paper or calculate in your head. What do you notice about the sums? Can you work out how to prove this?

### Comment

In the end, you will have selected exactly one number from each row, but none of these numbers appear in the same column. Find an easy set of five numbers from the grid that have this property.