7 ms·
6174 it's the only real solution of this system of equations: 9 ≥ a ≥ b ≥ c ≥ d ≥ 0 abcd - dcba = ABCD
by juanpablo 18y ago
6174 it's the only real solution of this system of equations:
9 ≥ a ≥ b ≥ c ≥ d ≥ 0
abcd - dcba = ABCD
- Retric 18y agoAre you positive that's true for all bases?
- jerf 18y agoThe statement as juanpaulo gives it has no hidden dependence on bases. It is all spelled out by the conditions. The symbols a b c d stand for any values, not the "actual digits" 0-9, which are also merely placeholders for values with no "true meaning" of their own.
- Retric 18y agoHe is using both digits and the nubers that sequence of digits represents in that equation. In base 10, 7641 - 1467 = 6174. In base 11, 7641 - 1467 = 4808. Finding tricks that work in base 10 is interesting, but it's a much more fun to look for patterns that work across several number systems. A simple example is for any base > 3, (base - 1) times x where base > x > 1; you get a 2 digit number [x - 1],[base - x]
- jerf 18y agoNo, they are not. The symbols in the equation are simply numbers, and "9 ≥ a ≥ b ≥ c ≥ d ≥ 0" constrains them to 0-9. You are mistaking the map for the territory, sort of. The positional aspects of the number system get encoded the equations and then the mere "numbers" don't matter anymore.
- jmathes 18y agoYes they are. Where he meant 1000a+100b+10c+d he wrote abcd.
- Retric 18y agoI think we are talking past each other. In base ten if you start with 1234 and cycle though asdf - fdsa > new number you hit a single stable number 6174 . In base 11 using 6174 you cycle: 4808, 87A3, 7094, 9272, 3098, 9452, 7094 (cycle) I was thinking of a http://en.wikipedia.org/wiki/Logistic_map http://en.wikipedia.org/wiki/Logistic_map for this equation abcd - dcba > might be interesting across different bases.