Easy · Worked puzzle
Undo the division first
Turn a bracketed division into a short list of number pairs.
(□ + □) ÷ 3 = 4
4 distinct solutions · 2 blanks
Play this puzzleTry the board first, or open the hints below at your own pace. No answers are shown until you choose to reveal them.
Before you play
- Each blank takes one digit from 0 to 9. Choices may be repeated.
- Follow the printed brackets and the order of operations. Each division must be exact. Division by zero is never allowed.
- Find all 4 distinct solutions. Reordering terms of the same addition or multiplication counts once. Subtraction, division and bracket structure still matter.
- Play without an account. Progress stays in this browser; the Lobby’s Continue button resumes an unfinished game. Web Hint and Reveal are free.
Show a starting hint
If a sum divided by three is four, what was the sum?
Read the worked approach
- The brackets say to add the two blanks before dividing by three. Reverse the final operation: the sum must equal 4 × 3 = 12.
- List pairs that add to twelve, keeping the smaller number first. The first legal pair is 3 and 9; a smaller first number would force the other above the keypad limit of nine.
- Continue with 4 and 8, 5 and 7, and 6 and 6. Each sum is twelve, so each gives an exact quotient of four.
- Stop at the equal pair. Continuing with 7 and 5 only swaps an addition you already found. This leaves four distinct solutions, not seven ordered arrangements.
A common trap
Dividing just the second blank by three ignores the brackets. Also, 6 + 6 is allowed: a digit does not get used up.
Carry this idea to the next puzzle
Undo a fixed outer operation, then search the smaller problem inside the brackets.
Reveal all 4 solutions
One representative of each distinct solution is shown. Other accepted orders of the same addition or multiplication are not repeated.
- (9 + 3) ÷ 3 = 4
- (8 + 4) ÷ 3 = 4
- (7 + 5) ÷ 3 = 4
- (6 + 6) ÷ 3 = 4
Check one answer, step by step
(9 + 3) ÷ 3 = 4
- 9 + 3 = 12
- 12 ÷ 3 = 4