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Four Dozen Camper Conclusion (Posted on 2023-04-18) Difficulty: 2 of 5
• The four 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.

Determine the total number of campers in each cabin.

See The Solution Submitted by K Sengupta    
Rating: 3.3333 (3 votes)

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Solution solution | Comment 2 of 3 |
A picture is worth many words:

       R   O   Y   G   B   P
    13-x  10   . = .   x   x+2

Either B has 6 and R has 7 or vice versa, since the smallest is 6.

There are 48 campers in all, an even number, and since Y = G, Y+G is an even number, and O (Orange), at 10, is even. Therefore R+B+P must be even.

If R were 7, it would be the only odd number, so R must be the even choice, 6; then B and P would be 7 and 9 respectively, two odd numbers that add up to the even 16.

       R   O   Y   G   B   P
       6  10   . = .   7   9
So far we've accounted for 32 campers out of the 48, so Y+G must be 16, evenly split between the two:

       R   O   Y   G   B   P
       6  10   8   8   7   9

  Posted by Charlie on 2023-04-18 09:07:52
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