Hard · Worked puzzle

Three factors, one small subtraction

Organise a four-blank puzzle by product and avoid counting rearrangements.

Mathoji.com · 16 October 2026 · Math checked against the game’s rules

□ × □ × □ − □ = 74

5 distinct solutions · 4 blanks

Try 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 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.

Show a starting hint

Before the subtraction, the product must be between seventy-four and eighty-three.

Read the worked approach

Write abc = 74 + d. The final digit limits the product to the interval 74–83. Zero cannot appear among the three factors because the product is positive.
Only 75, 80 and 81 in this interval split into three factors from one to nine. The other candidates contain a prime factor larger than nine.
For 75 use 3 × 5 × 5 and subtract 1. For 80 use 2 × 5 × 8 or 4 × 4 × 5 and subtract 6. For 81 use 1 × 9 × 9 or 3 × 3 × 9 and subtract 7.
There are five unordered triples. Putting the same triple in a different order repeats a multiplication, so Mathoji keeps it as the same solution.

Do not forget one as a factor. The triple 1, 9, 9 is as valid as a triple with three larger factors.

For a chain of multiplications, list sorted factor triples. This makes a four-blank puzzle manageable.

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 × 9 × 1 − 7 = 74

Found a problem with an explanation? Tell us which step needs a look.