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42Every Way to Make 10

The answer to life, the universe, and everything. There are exactly 42 ways to add whole numbers up to 10 — split below by the biggest number in each.

Practice — any partition

Warm up with the two free-play games before diving into a set.

Find all 42 — with walls

10 dots in a row, 9 spaces between them. Drop walls in to break the row into groups — the numbers add up to 10 every time. There are exactly 42 different partitions to find. (Same group sizes in a different order counts as the same partition.)

Found 0 / 42 10 = 10

The 42 — by biggest number

Tap a set to open it. Each set holds every partition whose biggest number is that value.

1Just ones1 partition

Build with 1 to 1

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

2With twos5 partitions

Build with 1 to 2

2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 = 10

2 + 2 + 2 + 1 + 1 + 1 + 1 = 10

2 + 2 + 2 + 2 + 1 + 1 = 10

2 + 2 + 2 + 2 + 2 = 10

Games for this set

3With threes8 partitions

Build with 1 to 3

3+1+1+1+1+1+1+1=10play coming soon
3+2+1+1+1+1+1=10play coming soon
3+2+2+1+1+1=10play coming soon
3+2+2+2+1=10play coming soon
3+3+1+1+1+1=10play coming soon
3+3+2+1+1=10play coming soon
3+3+2+2=10play coming soon
3+3+3+1=10play coming soon
4With fours9 partitions

Build with 1 to 4

4+1+1+1+1+1+1=10play coming soon
4+2+1+1+1+1=10play coming soon
4+2+2+1+1=10play coming soon
4+2+2+2=10play coming soon
4+3+1+1+1=10play coming soon
4+3+2+1=10play coming soon
4+3+3=10play coming soon
4+4+1+1=10play coming soon
4+4+2=10play coming soon
5With fives7 partitions

Build with 1 to 5

5+1+1+1+1+1=10play coming soon
5+2+1+1+1=10play coming soon
5+2+2+1=10play coming soon
5+3+1+1=10play coming soon
5+3+2=10play coming soon
5+4+1=10play coming soon
5+5=10play coming soon
6With sixes5 partitions

Build with 1 to 6

6+1+1+1+1=10play coming soon
6+2+1+1=10play coming soon
6+2+2=10play coming soon
6+3+1=10play coming soon
6+4=10play coming soon
7With sevens3 partitions

Build with 1 to 7

7+1+1+1=10play coming soon
7+2+1=10play coming soon
7+3=10play coming soon
8With eights2 partitions

Build with 1 to 8

8+1+1=10play coming soon
8+2=10play coming soon
9With nines1 partition

Build with 1 to 9

9+1=10play coming soon
10Just ten1 partition

Build with 1 to 10

10=10play coming soon

Watch

The narrated video version (coming soon).