Four Numbers That Add Up to 10: Examples and Puzzle Challenges
Four numbers that add up to 10 include 1 + 2 + 3 + 4, 2 + 2 + 3 + 3, and 1 + 1 + 4 + 4. The possible combinations depend on whether you allow repeated numbers, zero, or negative numbers. This article lists every combination under clear constraints, shows a few quick puzzles with answers, and explains how the same idea drives the Make 10 game.
1. Quick examples
Here are three valid ways to make 10 with four numbers, shown on tiles that match the game:
2. Four numbers from 1 to 4 that total 10
If every number is 1, 2, 3, or 4 and repeated numbers are allowed, there are exactly five combinations. We list combinations ignoring order, so 1 + 2 + 3 + 4 and 4 + 3 + 2 + 1 count as the same combination.
- 1 + 1 + 4 + 4 = 10
- 1 + 2 + 3 + 4 = 10
- 1 + 3 + 3 + 3 = 10
- 2 + 2 + 2 + 4 = 10
- 2 + 2 + 3 + 3 = 10
On a game board, placement still matters: the same four tiles must occupy four consecutive cells in a straight line before they count. The arithmetic combination alone is not enough.
3. Four positive whole numbers that total 10
Allowing any positive whole number from 1 to 9 (with repeats, ignoring order) gives nine combinations. Each one sums to 10.
- 1 + 1 + 1 + 7 = 10
- 1 + 1 + 2 + 6 = 10
- 1 + 1 + 3 + 5 = 10
- 1 + 1 + 4 + 4 = 10
- 1 + 2 + 2 + 5 = 10
- 1 + 2 + 3 + 4 = 10
- 1 + 3 + 3 + 3 = 10
- 2 + 2 + 2 + 4 = 10
- 2 + 2 + 3 + 3 = 10
If all four numbers must be different positive integers, the only combination is 1 + 2 + 3 + 4. Every other entry in the list repeats at least one value.
4. What changes when zero or negative numbers are allowed?
The examples below are general arithmetic. They are not game tiles: Make 10 never uses zero, and negative numbers appear only in Level 2 (−1 and −2) and Level 3 (−1, −2, and −3).
Zero examples
Negative-number examples
With unrestricted integers, there are infinitely many combinations. For example, 100 + (−90) + 1 + (−1) = 10. The lists above stay finite only because they restrict the allowed values.
5. Try these five missing-number challenges
Each puzzle has one missing number. Open a disclosure to check your answer.
1 + 2 + 3 + __ = 10
2 + 2 + __ + 4 = 10
1 + __ + 3 + 3 = 10
8 + 5 + (−1) + __ = 10
9 + 6 + (−2) + __ = 10
6. How this applies to Play Make 10
Make 10 turns this arithmetic into a board game. You drop numbered tiles into seven columns. To clear tiles, exactly four consecutive tiles in a straight line — horizontal, vertical, or diagonal — must total 10.
When a valid line clears, tiles above fall into the empty cells. If those falling tiles form a new line that also totals 10, you score a chain with bonus points. So a correct combination like 2 + 2 + 3 + 3 only helps when those four tiles actually sit in a connected line on the board.
Level 1 uses the numbers 1 through 4, so all of its matches come from the five combinations in section 2. Level 2 adds 5 through 9 plus −1 and −2, and Level 3 adds −3, opening up many more combinations — including the negative examples above. Zero is never a tile.
Play Make 107. Short FAQ
What four numbers add up to 10?
Common answers include 1 + 2 + 3 + 4, 2 + 2 + 3 + 3, and 1 + 1 + 4 + 4. The full list depends on which numbers you allow (see sections 2 and 3).
Can the numbers repeat?
Yes. In both the math examples and the game, repeated numbers are allowed. For example, 2 + 2 + 3 + 3 = 10 uses two 2s and two 3s.
What if all four numbers must be different?
With positive whole numbers, the only combination of four different numbers that totals 10 is 1 + 2 + 3 + 4.
Can I use zero or negative numbers?
In general arithmetic, yes — zero and negatives both work and create infinitely many combinations. In Make 10, zero is never available; negative numbers appear only in Level 2 and Level 3.