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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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Hints/Tips Too much information Comment 3 of 3 |
Since only two cabins share the same number of campers, there must be 5 cabins with 6, 7, 8, 9 and 10 campers.  This accounts for 40 campers, so the 6th cabin must have 8 campers.

Thus, the two smallest cabins must have 6 and 7 campers.  We did not need to be told that the total of the two smallest cabins was 13.  It would have been sufficient to just tell us that they were red and blue.

Since 6 and 7 are red and blue, and yellow and green both have 8, then 9 and 10 must be purple and orange. The only way that purple can have two more than blue is if Blue is 7 and Purple is 9.  So, there is no need to be told that Orange has 10. 

The following equivalent formulation is solvable with two less pieces of information:

• Four dozen campers live in 6 differently colored cabins.
• The smallest cabin has 6 campers and the largest has 10 campers.
• The yellow and green cabins are the only cabins with the same number of campers.
• The red and blue cabins have the least number of campers.
• The purple cabin has 2 more campers than the blue cabin.


Edited on April 18, 2023, 12:37 pm
  Posted by Steve Herman on 2023-04-18 09:48:07

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