Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

I'm Eight

Find a great variety of ways of asking questions which make 8.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

The Clockmaker's Birthday Cake

Stage: 2 Challenge Level:

Charles sent in his solution:

All the numbers together add up to $1+2+3+...+12=78$. There are six couples, each with the same total amount, so this must be $78/6=13$. So each couple's numbers add up to $13$.

I'm going to write the pairs in brackets, like this ( , ). The first number is the one for the man, and the second for the woman. So we know we have $(12, 1)$ and $(6, 7)$. We want the ladies' numbers and the men's numbers each to add up to $78/2=39$. Here's a way we could do it:

$(12, 1) (6, 7) (2, 11) (10, 3) (5, 8) (4, 9)$

And $12+6+2+10+5+4=39=1+7+11+3+8+9$.