The daily equation · Expert
October 12, 2026
One shared puzzle. Find every way to make it true.
(□ × □ + □) ÷ □ + 3 = 84
2 distinct solutions · 4 blanks · Expert
Play this daily puzzleBefore 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 2 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.
A way to begin
Treat each bracket as a quantity. Undo fixed operations outside the brackets, then look for factor pairs or sums that fit the allowed digits.
This equation has 4 blanks and 2 distinct solutions. List your cases systematically and use the green rows to avoid repeating a solved case. Explore this solving method.
Reveal all 2 solutions
One representative of each distinct solution is shown. Other accepted orders of the same addition or multiplication are not repeated.
- (9 × 8 + 9) ÷ 1 + 3 = 84
- (9 × 9 + 0) ÷ 1 + 3 = 84
Check one answer, step by step
(9 × 8 + 9) ÷ 1 + 3 = 84
- 9 × 8 = 72
- 72 + 9 = 81
- 81 ÷ 1 = 81
- 81 + 3 = 84