Hard · Worked puzzle

A large target with only three answers

Factor the target before filling the two sums in brackets.

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

(□ + □) × (□ + □) = 221

3 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 3 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

Each bracket is a sum of two digits, so neither bracket can exceed eighteen.

Read the worked approach

Treat the two brackets as S and T. They satisfy ST = 221. The factorisation 221 = 13 × 17 fits the maximum sum of eighteen for each bracket.
The alternative positive factor pair, 1 and 221, cannot fit. Thus one bracket must total thirteen and the other seventeen.
Seventeen has just one unordered digit pair: 8 + 9. Thirteen has three: 4 + 9, 5 + 8 and 6 + 7. Pair each of those with 8 + 9.
Swapping terms inside an addition, or swapping the two whole sums in the product, preserves the same expression structure and does not create another solution. There are three distinct results.

Moving a single digit from one bracket to the other is not the same as swapping the two whole brackets. Recheck both sums after such a move.

A large target can be easier than a small one when its factorisation sharply limits the bracket values.

Reveal all 3 solutions

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

(9 + 8) × (9 + 4) = 221

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