Talk:Bentley's number

What is this number meant to represent in the story? I assume it was meant to be the total count of wheels on all ten counters. If this is so, a careful reading of the story reveals that the value listed here can not be correct. Recall that the first counter contains 1 wheel, and each succeeding counter has a number of wheels that is a power of 10. It follows then that the count of all wheels must end in a 1, yet the number listed here must end in a zero.

Remember the first counter has 1 wheel, and can be in 10 states, the second counter has 10 wheels and can be in 10,000,000,000 states, the third counter has 10,000,000,000 wheels and can be in 10^10^10 or trialogue states, the fourth counter has a trialogue wheels and can be in 10^^4 or a tetralogue states, etc. In general the nth counter has 10^^(n-1) wheels and 10^^n states. Therefore the tenth counter must have 10^^9 or an ennalogue states. So Bentley's number should be redefined as (10^^0)+(10^^1)+(10^^2)+ ... +(10^^7)+(10^^8)+(10^^9), where b^^0 := 1. If the summation indexes were changed from i=1,10 to i=0,9, it would give the total number of wheels on all ten counters. If anyone agrees that this number is incorrectly defined perhaps it could be changed.

74.105.180.128 18:50, January 27, 2012 (UTC) Sbiis Saibian