Complex Modulo

The sign below was found by my mother on a recent drive down I-94. She was doing some Road Sign Math hunting and came across this sign and found the combination of numbers very compelling. This had to be a winning sign she thought, but she didn't see how. Not one to give up quickly she took the picture anyway and decided to leave it to further analysis.



Did you find it yet? This one is not easy. There are a lot of numbers here, rather big numbers at that. Too many numbers to just subtract two and get 1 as we can do on many signs. The answer to this sign eludes you for a long time. However, there are two numbers on here that ultimately give us the solution. The 1 is always tempting in Road Sign Math. There are many ways to get to a one, but nothing seemed to fit here. The 10 is also very compelling since it can be used in so many ways. The answer then becomes clear!

$$(76 + 77 + 78) \bmod 10 = 1$$

The 10 and the 1 are the key. Adding 76, 77 and 78 yields 231 which results in 1 after applying modulo 10. Voila! Valid sign.

This sign was found on I-94 westbound in Minnesota.