Problem 9 · 2024 Math Kangaroo
Medium
Logic & Word Problems
sum-constraintwork-backward
Lisa writes the numbers 1, 2, 4, 5 and 6 in the circles of the pattern, using each number exactly once. Along each of the three straight lines the numbers add up to 11. Which number does she write in the circle with the question mark?
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Answer: C — 4
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Hint 1 of 2
The two bottom circles sit on a line by themselves, so they must add to 11.
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Hint 2 of 2
Find which pair from the numbers adds to 11, then use the other two lines through the centre to pin down the question mark.
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Approach: use the line totals of 11 to solve for the centre
- The bottom two circles form one line, so they add to 11: that's 5 and 6.
- The remaining numbers 1, 2, 4 fill the two top circles and the centre, totalling 7.
- Each slanted line is (top) + (centre) + (bottom) = 11; adding both gives 7 + centre = 11.
- So the centre is 4 (C).
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