Problem 24 · 2022 Math Kangaroo
Stretch
Algebra & Patterns
substitutionsum-constraint
Cards of the same colour always hide the same number. When the three hidden numbers in a row are added, you get the number written to the right of that row (see diagram). Which number is hidden under the black card?
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Answer: D — 12
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Hint 1 of 3
Every card of the same colour hides the same number, so think of one secret number per colour.
Still stuck? Show hint 2 →
Hint 2 of 3
Compare two rows that are almost the same to find one colour's number first.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you know grey and white, the black card is just its row total take away the other two.
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Approach: compare rows to peel off one colour at a time
- The top row is grey + white + white = 34, and the bottom row is white + grey + grey = 26.
- Both rows use one extra grey instead of one extra white, and they differ by 34 − 26 = 8, so a white card is 8 more than a grey card.
- Trying small numbers that fit grey + 2 whites = 34: grey = 6 and white = 14 works (6 + 14 + 14 = 34).
- The middle row grey + white + black = 32, so black = 32 − 6 − 14 = 12 — answer D.
For older kids (with letters)
Let grey = g, white = w, black = k. From g + 2w = 34 and 2g + w = 26 you get g = 6, w = 14, then k = 32 − g − w = 12.
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