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## Four Dozen Campers

Math brain teasers require computations to solve.

 Puzzle ID: #7474 Fun: (2.7) Difficulty: (1.86) Category: Math Submitted By: hprulz

The 4 dozen campers in the junior division live in 6 differently colored cabins along Miller's Pond. The smallest cabin has 6 campers, and the orange cabin is the largest with 10 campers. The yellow and green cabins are the only cabins with the same number of campers. The 13 youngest campers are in the red and blue cabins with the least number of campers. The purple cabin has 2 more campers than the blue cabin.

How many campers are in each cabin?

Orange = 10
Purple = 9
Yellow = 8
Green = 8
Blue = 7
Red = 6

From the second and fourth lines, you know that one cabin contains 10 campers and the two smallest cabins contain 7 and 6 campers. This leaves 48 - 10 - 7 - 6 = 25 campers unaccounted for. You know that the yellow and green cabins have the same number of campers (Statement 3) and that the purple cabin has either 8 (6+2) or 9 (7+2) campers (Statement 5). There can't be 8 in the purple cabin because that would leave 17 for the yellow and green cabins, which doesn't divide by two evenly. Therefore there are 9 campers in the purple cabin leaving 8 in each of the yellow and green cabins. This also means that there are 7 campers in the blue cabin, from the last statement. All that's left is the red cabin, with 6 campers.

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