Some number fun

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 Lurkie (March 22, 2011, 13:45:26 PM):
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ETA: .... but just for interest, is there an elegant way of solving these chestnuts, or is inspection and a keen eye the only hope? They look a bit like simultaneous equations, and its almost as if they beg to be solved in a similar manner ... but, of course, they are not equations at all.

I'd love to learn an elegant way to solve these rotters. Roasting fork moments almost drove me to write some code to implement a brute force search to test lots and lots of possible combinations of operators for the given number sequence. Only problem is that there are gazillions of combinations. But this will still miss the problems where only a demented human brain will pick up a non-mathematical pattern.

 Tweefo (March 22, 2011, 13:56:00 PM):
Enough of these brilliant minds being wasted on games. Here is a real life number problem: My bank balance need to grow! Fast!
 Hermes (March 22, 2011, 14:29:48 PM):
Enough of these brilliant minds being wasted on games. Here is a real life number problem: My bank balance need to grow! Fast!
No problem, if

\$1 ○ \$3 ○ \$7 → \$353
\$2 ○ \$9 ○ \$8 → \$595
\$4 ○ \$8 ○ \$5 → \$193
\$6 ○ \$7 ○ \$4 → \$119
\$7 ○ \$4 ○ \$6 → \$239
then
\$3 ○ \$5 ○ \$7 → ?

 Lurkie (March 22, 2011, 14:47:13 PM):
Quote
No problem, if

\$1 ○ \$3 ○ \$7 → \$353
\$2 ○ \$9 ○ \$8 → \$595
\$4 ○ \$8 ○ \$5 → \$193
\$6 ○ \$7 ○ \$4 → \$119
\$7 ○ \$4 ○ \$6 → \$239
then
\$3 ○ \$5 ○ \$7 → ?

Hmm. Not good if the operators divide the numbers resulting in an infinitely diminishing balance. I suggest a new operator where ○=\$
 Mefiante (March 22, 2011, 15:46:33 PM):
Mathematically speaking, these problems aren’t especially interesting or edifying. At best, they can be used to illustrate some core mathematical ideas whose application is mostly cryptographic. And no, there is no fixed approach to them because the variety of possible schemes is virtually limitless.

That said, for the insatiably curious, frustrated and bagshot among us, here’s…

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'Luthon64