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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?

Throw a 100

Age 7 to 11
Challenge Level

There were two things to discover here:

  • Is it possible to total exactly 100 with the given set of numbers? 
  • If it is possible, how many ways can 100 be scored?

It took quite a lot of work to solve this seemingly easy problem as Amelia from Belchamp St. Paul Primary School shows in her calculations:

I tried lots of different combinations of numbers and the closest number I got was 101. Then I tried this:

  3x17=51
100-51=49
49-17=32
2x16=32
4x17=68
32+68=100

Tom from Brecknock Primary School used this strategy:

First I tried 40+39+24=103 then I tried 40+39+23=102
Next I tried all the possible ways to get rid of the extra 2.
I tried 100-16*2=68
I know that 17*4=68, so I added 68+32=100

Anisha from Eastbury Farm School in Hertfordshire, and Lisa, a pupil at W.C.P. School in Manchester, and Sarah-Jane of Belchamp St. Paul Primary School all found the same solution as Tom, but expressed it differently:

Their solution: 16+16+17+17+17+17=100

Are there any more possibilities? Are we sure?