• 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.
A picture is worth many words:
R O Y G B P
13x 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 20230418 09:07:52 