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 Odometer Sum of the Digits (Posted on 2006-01-19)
A mechanical six-digit car odometer has 6 wheels with the digits 0-9 on each wheel. Imagine taking the odometer out of the car and taking off the cover so you can see all the digits on all the wheels. Each row forms a six digit number. If the first row reads 123456, the next row would read 234567 and so on to the 10th row which would read 012345.

Consider the sum of the digits in each row. Is there a setting of the odometer that results in the sum of each row being the same?

If not, what's the best we can do? Let's define "best" as a setting where difference between the smallest sum and largest sum is minimized. What's the smallest odometer reading that achieves this minimum difference, and what is the difference value?

Finally, if we drop the "smallest odometer reading" requirement, then other than permutations of the wheels and rotations of the entire wheel set, how many distinct solutions are there? Or is this solution unique?

 See The Solution Submitted by Ken Haley Rating: 4.3333 (3 votes)

 Subject Author Date re(4): computer solution Ken Haley 2006-01-20 22:40:15 re(3): computer solution Charlie 2006-01-20 09:01:40 re(2): computer solution Charlie 2006-01-20 08:52:49 re: computer solution Ken Haley 2006-01-20 01:05:23 re: Spolier -- Best solution Ken Haley 2006-01-20 00:52:40 re(2): computer solution Eric 2006-01-19 19:54:03 re: computer solution Steve Herman 2006-01-19 16:12:20 Spolier -- Best solution Steve Herman 2006-01-19 16:00:09 computer solution Charlie 2006-01-19 15:02:44 Why is it an "odo" meter? Leming 2006-01-19 13:29:29 Best I could get playing with it Jer 2006-01-19 12:39:42

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