3 ms·
I wonder how many numbers between 0 and 9! (if any) cannot be generated by each method.
by gphil 17y ago
I wonder how many numbers between 0 and 9! (if any) cannot be generated by each method.
- gjm11 17y agoActually, not 9! but (1+2) x 3 x ... x 9, because multiplying by 1 is no use. According to my brute-forcer, you can get everything from 0 to 2283 but not 2284. The first few missing numbers are 2284, 2758, 2812, 2902, 2932, 3076, 3119, 3137, 3208. The first gap of more than one number is that you can't do either 3802 or 3803. The first gap of >= 3 numbers is 4280-4282. The total number of different achievable nonnegative integers is 14026. The biggest two are 9! and (3/2)x9!, unsurprisingly.
- gjm11 17y agoI regret that my program doesn't record how it achieved each number, so without running it again I can't tell you how to get 2036 or 2086 as per 3pt14159's request above. It's at http://pastie.org/767276 http://pastie.org/767276 in case anyone cares.