The daily equation · Master
October 8, 2026
One shared puzzle. Find every way to make it true.
√(□) × □ + □ × 4 = 1
4 distinct solutions · 3 blanks · Master
Play this daily puzzleBefore you play
- Each blank accepts one of these complete expressions: 012341/21/32/33/2√2√3∛2. Choices may be repeated.
- Follow the printed brackets and the order of operations. Fractional intermediate values are allowed. 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.
A way to begin
Read the expression choices before starting. Simplify any familiar roots, then look for fraction or root pairs that make a useful whole number.
This equation has 3 blanks and 4 distinct solutions. List your cases systematically and use the green rows to avoid repeating a solved case. Explore this solving method.
Reveal all 4 solutions
One representative of each distinct solution is shown. Other accepted orders of the same addition or multiplication are not repeated.
- √(1) × 1 + 0 × 4 = 1
- √(4) × (1/2) + 0 × 4 = 1
- √((1/2)) × (√2) + 0 × 4 = 1
- √((1/3)) × (√3) + 0 × 4 = 1
Check one answer, step by step
√(1) × 1 + 0 × 4 = 1
- 1 × 1 = 1
- 0 × 4 = 0
- 1 + 0 = 1
The step check shows decimal approximations where needed; fraction and root keys above retain their exact written form.