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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?

1, 2, 3, 4, 5

Age 7 to 11
Challenge Level

Bethany from Tattingstone, Douglas from Burgoyne Middle School and Amelia who goes to Norland Place School all decided the answer to this problem was the number 1. Douglas said:

First I worked out which things seemed to make a good choice to start looking at. Multiplying by 1 seemed to be a good idea, although I found that this didn't make any whole numbers so I scrapped it.
Then I tried multiplying by two. The best answer I found was three (51/34x2).
Finally I tried multiplying by four. I found the best answer, it was one (13/52x4).
I didn't try five because I knew it wouldn't make less than one.This means the answer is 13/52x4.

Amelia told us:

Think of a big number to divide by. Try something ending in 4 as it will be divisible by 2.
After lots of experimenting I came up with 51x2/34=3.
I also came up with 52/13x4 but my teacher explained that this would only equal 1 if I could put brackets
around (13x4) or else it would be actually equal to 16.

Bethany used a calculator to move the numbers around and try different combinations. She arrived at 13x4/52.

Fantastic! Three different solutions to admire.