The daily equation · Expert
August 28, 2026
One shared puzzle. Find every way to make it true.
□ × (□ + □) ÷ □ = 78
3 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 3 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 3 distinct solutions. List your cases systematically and use the green rows to avoid repeating a solved case. Explore this solving method.
Reveal all 3 solutions
One representative of each distinct solution is shown. Other accepted orders of the same addition or multiplication are not repeated.
- 6 × (9 + 4) ÷ 1 = 78
- 6 × (8 + 5) ÷ 1 = 78
- 6 × (7 + 6) ÷ 1 = 78
Check one answer, step by step
6 × (9 + 4) ÷ 1 = 78
- 9 + 4 = 13
- 6 × 13 = 78
- 78 ÷ 1 = 78