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Sam Loyd - Columbus Problem
I found the instructions for the Sam Loyd - Columbus problem vague and misleading. The drawing shows the dots as being at the mid-height of the numbers, not at the bottom as if they were decimals. In your instructions you represent the dots where you find them if they were used as decimals. Further, in your solution you use the dots to represent repeating digits. When I went to school we were taught to use a horizontal bar for this purpose. If you are going to use non-standard, or obsolete, rules for notation, it would be nice if you specified what they were.
Re: Sam Loyd - Columbus Problem
The last follows the definition given above.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.