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Exploring Wild & Wonderful Number Patterns

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Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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?