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Alphabetical Angle

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

There are 24 arrangements of the letters in the word ANGLE with A as the first letter (the number of ways of arranging the other 4 letters is $4\times3\times2\times1$). In alphabetical order AEGLN is first and ANLGE is last. ANLEG is the 23rd and hence ANGLE is in the 22nd position on the list.

This problem is taken from the UKMT Mathematical Challenges.