Problem 113

Comments

This one took forever! It’s been several days since I’ve completed a problem so I’m feeling pretty good about finishing one again. I’ve had to do this one several times.

I had to do several things to make this one come out. I used dictionaries to keep track only of the last digit of the numbers.

Because those numbers that are the same number in each digit would be counted twice: first in the up numbers and second in the down numbers. Those were eliminated at the end.

With the completion of this problem, I’ve now made it to Level 5!! Woopee!

Code

Udict = dict(zip(range(1,10),[1]*9))
Ddict = dict(zip(range(1,10),[1]*9))
Ddict[0] = 0
count = 18

for i in xrange(99):
	newdict = dict(zip(range(10),[0]*10))
	for key in Udict.iterkeys():
		for x in range(key, 10):
			newdict[x] += Udict[key]
	Udict = newdict.copy()
	for value in Udict.itervalues():
		count += value

for i in xrange(99):
	newdict = dict(zip(range(10),[0]*10))
	for key in Ddict.iterkeys():
		for x in range(key+1):
			newdict[x] += Ddict[key]
	Ddict = newdict.copy()
	for value in Ddict.itervalues():
		count += value
			
print count - (100*9)