One Line Elf, Two Line Elves, Three Line Elves...
I have a number of slave elves. They all either have Knobbly Knees, Baseball Eyes, Pointy Ears or a Wart on the nose. One day, Victor comes into my slave elf lab. He wants to help me classify the elves. Each elf can have at most 3 features, but a special type of elf called the "One Line Elf" has all four features. After some counting, Victor finds 20 elves with Baseball Eyes, 24 With Pointy Ears, 10 With A wart on the nose and 5 with knobbly knees. How many elves are there, including the "One Line Elves"? (Look for the minimal number)
P.S. (I wrote this to practise for my compo)
The answer is 24.
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Clearly we need at least 2 4 elves, considering that there are 2 4 with the feature pointy ears. Now we can easily create a 2 4 -elf configuration by greedily taking as many features as possible to each elf. This gives 5 One Line Elf, 5 elves with all but knobbly knees features, 1 0 elves with baseball eyes and pointy ears, and 4 elves with only pointy ears, which is a valid configuration. Thus the answer is 2 4 .