Which Card Must We Have?
There are 7 cards, each containing the numbers 1, 2, 3 or 4.
Each number appears at most twice.
The cards are arranged so that there are
cards between the cards numbered
.
The numbers 3 and 4 appear at the extreme ends
Which card could NOT appear exactly once?
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1 solution
Now, it remains to show that we cannot be missing a 3. Suppose we were missing a 3. Then, because we have two 4's, the cards must look as such:
However, it's clear that we cannot fit 1's and 2's in the 4 consecutive spaces.