Throw a 100
Problem
There is to be a grand prize at the ring toss booth for the person who can score exactly 100 with 10 rings or fewer.
More than one ring can land on a number.
The numbers are those shown on the board.
Can you score 100? Is there more than one way to do it?
Student Solutions
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
Their solution: 16+16+17+17+17+17=100
Are there any more possibilities? Are we sure?