Problem 25 · 2010 Math Kangaroo
Stretch
Logic & Word Problems
caseworksum-constraint
Six-legged, seven-legged and eight-legged octopuses serve Neptune, the king of the sea. The seven-legged ones always lie, and the six-legged and eight-legged ones always tell the truth. One day four octopuses meet. The blue one says, “We have 28 legs altogether.” The green one says, “We have 27 legs altogether.” The yellow one says, “We have 26 legs altogether.” The red one says, “We have 25 legs altogether.” How many legs does the red octopus have?
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Answer: B — 7
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Hint 1 of 2
The six- and eight-legged ones tell the truth, so they all state the real total.
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Hint 2 of 2
Test each claimed total and see which makes a consistent set of leg counts.
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Approach: find the consistent true total
- Truth-tellers (6 or 8 legs) all name the real total; liars (7 legs) name something else.
- If the real total is 27, the truthful one has 6 legs and the other three lie with 7 legs each (3x7+6 = 27).
- The red octopus is one of the liars, so it has 7 legs.
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