Talk:Sum to 100: Difference between revisions
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:: For performance note that it is not necessary to generate the strings to count the solutions. There are 2 * 3 ** (base-2) possible strings. In base 2 the maximum value is 1 the minimum value -1. 0 can not be generated so 66% of values can be represented. The number of possible strings increases exponentially with the base, so to stretch this task for extra credit we could ask what is the %age in base 64, or 60 if we want to be Babylonian, or why not more. I often read that we use base 10 because we have 10 fingers, is there any archeological evidence that the Babylonians were severely deformed? --[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 12:54, 25 February 2017 (UTC) |
:: For performance note that it is not necessary to generate the strings to count the solutions. There are 2 * 3 ** (base-2) possible strings. In base 2 the maximum value is 1 the minimum value -1. 0 can not be generated so 66% of values can be represented. The number of possible strings increases exponentially with the base, so to stretch this task for extra credit we could ask what is the %age in base 64, or 60 if we want to be Babylonian, or why not more. I often read that we use base 10 because we have 10 fingers, is there any archeological evidence that the Babylonians were severely deformed? --[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 12:54, 25 February 2017 (UTC) |
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:::: I know you're kidding, and of course the Babylonians had ten fingers, but the assumption is that they realized base 60 would be an advantageous base and chose it with intention, rather than just going with the number of digits they were born with. I don't know of anyone else who independently adopted base 60, but base 10 was far from universal around the world; the Mayans used base 20, the Hawaiians base 12, some other Pacific Islanders base 4... --[[User:Markjreed|Markjreed]] ([[User talk:Markjreed|talk]]) 00:54, 25 March 2024 (UTC) |
:::: I know you're kidding, and of course the Babylonians had ten fingers, but the assumption is that they realized base 60 would be an advantageous base and chose it with intention, rather than just going with the number of digits they were born with. I don't know of anyone else who independently adopted base 60, but base 10 was far from universal around the world; the Mayans used base 20, the Hawaiians base 12, some other Pacific Islanders base 4... --[[User:Markjreed|Markjreed]] ([[User talk:Markjreed|talk]]) 00:54, 25 March 2024 (UTC) |
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:::: Apparently there ''is'' indeed some archeological evidence that nearly all Babylonians had ''twelve'' finger knuckles on the back of each hand, as well as ''five'' digits on the other side. And, albeit less impressively, ancient Mayan skeletons show that both of their hands (also with five digits apiece) were also connected to the rest of them by so-called "wrists"... (IKUAKAT) --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 04:42, 25 March 2024 (UTC) |
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==complete list of solutions for '''9'''== |
==complete list of solutions for '''9'''== |
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