The daily equation · Hard
October 16, 2026
One shared puzzle. Find every way to make it true.
(□ + □) × (□ − □) + 5 = 90
5 distinct solutions · 4 blanks · Hard
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 5 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 5 distinct solutions. List your cases systematically and use the green rows to avoid repeating a solved case. Explore this solving method.
Reveal all 5 solutions
One representative of each distinct solution is shown. Other accepted orders of the same addition or multiplication are not repeated.
- (9 + 8) × (5 − 0) + 5 = 90
- (9 + 8) × (6 − 1) + 5 = 90
- (9 + 8) × (7 − 2) + 5 = 90
- (9 + 8) × (8 − 3) + 5 = 90
- (9 + 8) × (9 − 4) + 5 = 90
Check one answer, step by step
(9 + 8) × (5 − 0) + 5 = 90
- 9 + 8 = 17
- 5 − 0 = 5
- 17 × 5 = 85
- 85 + 5 = 90