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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.

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?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

The Clockmaker's Birthday Cake

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