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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 Itried 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

Below we will see what this means to other problem solvers.

Adam and Anthony from Moorfield Primary School also persevered until they were successful:

We tried loads of different possible solutions then we finally got:
40+17+17+16=100.

The boys used this first solution to find others. They took the greatest of the numbers (40) and then found different combinations of numbers that would total 40.

We used different numbers to make 40
24+16+17+17+16=100
23+17+17+17+16=100

Good work from everybody so far, but were these only possibilities? 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 think not:

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

Now have we seen this solution before anywhere?
Are there any more possibilities? Are we sure?