Tricky Test 2 Level 89

Overview

The screen shows a vertical addition puzzle titled "Complete the equation!" in white text near the top. There are three rows of three empty square boxes: the top row is the first addend, a plus sign sits on the left of the second addend row, and a horizontal line separates them from the third row, which is the sum. A small "7" is already filled into the units (rightmost) box of the result row. Below the puzzle is a tray of nine white number tiles, one each for the digits 1 through 9, plus a circular reset button and a grey SUBMIT button. The task is to drag tiles from the tray into the empty boxes so that the vertical addition is correct, using every digit 1-9 exactly once. This is a classic pandigital addition puzzle.

• Difficulty: Hard
• Estimated moves: 7

Step-by-Step Solution

1. Look at the units column first. The result's units digit is given as 7. The bottom addend's units tile is 8 (drag the 8 tile there). The top addend's units must be a digit that, when added to 8, ends in 7. Since 9 + 8 = 17, drag the 9 tile into the top addend's units box. This produces a carry of 1 into the tens column.
2. Move to the tens column. You need top-tens + bottom-tens + the carry of 1 to end in 6 (the result tens digit). The solution uses top-tens = 3 and bottom-tens = 2, because 3 + 2 + 1 = 6 with no further carry. Drag the 3 tile into the top addend's middle box and the 2 tile into the bottom addend's middle box.
3. Move to the hundreds column. With no carry from the tens column, the two hundreds digits must add up to 5 (the result hundreds digit). The only two unused digits that sum to 5 are 1 and 4. Drag 4 into the top addend's hundreds box and 1 into the bottom addend's hundreds box.
4. Check the full equation on screen: 439 + 128 = 567. Verify: units 9 + 8 = 17 (write 7, carry 1); tens 3 + 2 + 1 = 6; hundreds 4 + 1 = 5. The equation balances and uses digits 1 through 9 exactly once.
5. Tap the SUBMIT button to confirm and clear the level.

Strategy & Reasoning

The puzzle looks like a free-form trial-and-error, but it is actually constrained enough to solve column by column from right to left, the way you would do normal long addition. The given 7 in the result's units box is the anchor. Because only digits 1-9 are available (no 0), the only way to get a units result of 7 when adding two single digits is a pair that sums to 17 (i.e. 9 + 8), which forces a carry. This immediately fixes the units column.

Once the units column is fixed, the tens column is nearly as constrained: with a carry of 1 and a target tens result of 6, the two tens digits must sum to 5. Combining that with the remaining digits and the no-carry condition leads to 3 and 2. Finally the hundreds column is left with the two biggest remaining digits that sum to the result's hundreds digit, 5, which can only be 1 and 4.

The alternative arrangement 139 + 428 = 567 also works arithmetically and uses the same digits, but the recorded solution fills the top addend as 439 and the bottom as 128. Either order is accepted by the puzzle as long as the digits are placed correctly. Guessing randomly from the tray is slow and risks filling a box wrong; working right-to-left with carries is the reliable path.

Tips & Common Mistakes

• Mistake: Ignoring the carry from the units column. Correct approach: Remember that 9 + 8 = 17 produces a carry of 1 into the tens column; forgetting it makes the tens column impossible.
• Mistake: Trying to use the digit 0. Correct approach: The tray only contains 1 through 9; there is no 0, so every column must be filled with digits from that set.
• Mistake: Placing digits randomly and pressing SUBMIT. Correct approach: Solve column by column from right to left, checking the sum at each step before moving on.
• Mistake: Forgetting that each digit can only be used once. Correct approach: Keep track of which tiles you have already placed; the tray should be empty when the equation is complete.