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Solutions 151 - 200

Project Euler 172 Solution

Project Euler 172 Solution

Project Euler 172: Investigating numbers with few repeated digits


How many 18-digit numbers n (without leading zeros) are there such that no digit occurs more than three times in n?

Project Euler 172 Solution

Runs < 2 seconds in Python.
from Euler import binomial
digits, base, max_r = 18, 10, 3

def nd(d,b):
   if b>1: 
      return sum(nd(d-r, b-1)*binomial(d,r) for r in xrange(min(d+1, max_r+1)))
   return d <= max_r

print "There are", nd(digits, base) * (base-1)/base,
print digits, "digit numbers such that no digit occurs more than", max_r,
print "times in base", base
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