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Throw a 100

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?