Problem 16 · 2012 Math Kangaroo
Medium
Logic & Word Problems
sum-constraintwork-backward
Frank laid out his dominoes as shown in the picture. (Dominoes that touch must always show the same number of points.) Before his brother George removed two dominoes, there were 33 points altogether. How many points is the question mark worth?
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Answer: C — 4
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Hint 1 of 2
Touching halves must match, so equal numbers run along where dominoes meet.
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Hint 2 of 2
Use that the whole chain held 33 points to pin down the hidden half.
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Approach: use matching ends and the total of 33
- Where two dominoes touch the pips are equal, which fixes most of the hidden values along the chain.
- Adding all the visible pips and using that the full set held 33 points leaves the question-mark half determined.
- Carrying out that bookkeeping gives the missing value.
- The question mark is worth 4.
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