NMO Problem 1

Algebra Level 5

A five-digit positive integer a b c d e 10 abcde_{10} ( a ≠ 0 a\neq 0 ) is said to be a range if its digits satisfy the inequalities a < b > c < d > e a<b>c<d>e . For example, 37452 37452 is a range. How many ranges are there? This problem is from the NMO.This problem is part of this set .


The answer is 8622.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

David Holcer
Mar 21, 2015 
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count=0
for i in range(10**4,10**5):
    i=str(i)
    if i[0]<i[1]>i[2]<i[3]>i[4]:
        count+=1
print count

:) cheap way again

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