# Math Problem #1

• Mar 10th 2012, 05:24 PM
Sarang
Math Problem #1
Help me please!!! Please explain me the easiest way to do this! Thanks!

How many ten-digit numbers composed only by digits 1, 2 or 3 satisfy the rule: "Any two adjacent digits differ by 1?"

Options:

a) 16
b) 32
c) 64
d) 80
e) 100
• Mar 10th 2012, 08:12 PM
Wilmer
Re: Math Problem #1
Is this for a competition, or homework?
• Mar 10th 2012, 10:33 PM
Sarang
Re: Math Problem #1
Maybe, teacher gave this for homework......
• Mar 11th 2012, 03:55 AM
Wilmer
Re: Math Problem #1
Can you at least write one such 10digit number?
• Mar 11th 2012, 10:13 AM
Sarang
Re: Math Problem #1
Grade 9 and 1212121212 is one example but the key is to find it out in the shortest amount of time.... Challenging the problem with brute force isn't gonna be logical. I was wondering if there would be an easier way such as any tricks, using algebra, etc.
• Mar 11th 2012, 10:49 AM
SpringFan25
Re: Math Problem #1
here is a hint, think in terms of pairs of digits.

here are two relevent facts for this problem:
A) every time you get a 2 the next pair of digits must be 32 or 12. in either case, you return to the number two after the next pair of digits.

B) the number must start either 12...., or 32....., or 2.... you can analyse each of these cases seperately using rule (A).