Easy · Worked puzzle

Two ways to reach eighteen

Use the size of the last blank to narrow a multiplication puzzle to two possibilities.

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

□ × 9 + □ = 18

2 distinct solutions · 2 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

The second blank can add at most nine. How close to eighteen must the multiple of nine be?

Read the worked approach

Call the first blank a and the second b. The equation is 9a + b = 18, with each blank a whole number from 0 to 9. Repeated numbers are allowed.
Because b is between 0 and 9, 9a must be between 9 and 18. That leaves a = 1 or a = 2. Starting with a = 0 would require b = 18, which is not on the keypad.
For a = 1, subtract 9 from 18 to get b = 9. For a = 2, the multiplication already reaches 18, so b = 0. These give 1 × 9 + 9 and 2 × 9 + 0.
Both are distinct: the fixed multiplier is nine, so moving the two blank values between their positions would change the expression. There are no other first-blank values inside the bound.

Doing the addition before the multiplication changes the problem. Multiply the first blank by nine before adding the second.

A single small remainder can put a strong bound on a multiplication. Work out that bound before trying digits.

Reveal all 2 solutions

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

1 × 9 + 9 = 18

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