Expert · Worked puzzle

Strip away the outside operations

Reduce a nested Expert equation to two nearby multiplication facts.

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

(□ × □ + □) ÷ □ + 4 = 77

2 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 2 distinct solutions. Reordering terms of the same addition or multiplication counts once. Subtraction, division and bracket structure still matter.
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Show a starting hint

Remove the final four first. How large can the numerator be?

Read the worked approach

Subtract four from seventy-seven. We need (ab + c) ÷ d = 73, or ab + c = 73d. The numerator is at most 9 × 9 + 9 = 90.
A divisor of two would require a numerator of 146, already too large. Zero is not a valid divisor. Thus d = 1 and ab + c = 73.
The product ab must be between 64 and 73. The only digit multiplication facts in that range are 8 × 8 = 64 and 8 × 9 = 72.
The first needs c = 9, and the second c = 1. The bracket becomes seventy-three, dividing by one leaves it unchanged, and adding four returns seventy-seven.

Subtract the outside constant from the target, not from a single blank inside the numerator.

Peel away operations in reverse order. A nested equation can reduce to a familiar multiplication-table search.

Reveal all 2 solutions

One representative of each distinct solution is shown. Other accepted orders of the same addition or multiplication are not repeated.

(8 × 8 + 9) ÷ 1 + 4 = 77

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