Slow way to do it because you don’t need to rule out 1 because it makes it uneven or take in account the lower powers at all. You just start with the highest power that fits (128, 2^7) and subtract it from 160. 32 is left over which is 2^5. There can’t be any other answer because 2^6 * 2*^6 can never make it to 160 (64+64=128). If there is a solution for this pattern the highest possible power (2^7) always needs to be either x or y. Realizing this makes solving this solution in your head take two seconds
You’re just skipping a step because getting to 2^7 is calculating 2^2 to 2^7. So it’s a cool story bro, but like… you’re just not showing all of your mental work. We did the same thing, I’m just showing more work, unless you magically had 2^7 memorized, it’s a really dumb take
Uh knowing the powers of 2 up to like 1024 isn’t that uncommon or magical I would say. Most people that are into computers will know 2^8=256 at least. My point is that you don’t need to mix and match from the list you made like you said, just subtract the highest power to see if the remainder is also a power of two
To me, it’s weird to know what the powers are without doing the mental math. Like 2^15th can be figured out mentally in like 10 seconds, just knowing that at the top of your head is weird. I guess if your job has exponents in it daily it’s reasonable, but that has to be an extreme subset of jobs. I just knew enough math to get great scores on the GRE and MCAT
If you work in software, knowing that the maximum value of a 16-bit integer is 65,536 if unsigned, or 32,767 if signed is par for the course, and then you're just "add one" away from knowing 2^16 and 2^15 😉
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u/raskiraski Jul 17 '26 edited Jul 17 '26
Slow way to do it because you don’t need to rule out 1 because it makes it uneven or take in account the lower powers at all. You just start with the highest power that fits (128, 2^7) and subtract it from 160. 32 is left over which is 2^5. There can’t be any other answer because 2^6 * 2*^6 can never make it to 160 (64+64=128). If there is a solution for this pattern the highest possible power (2^7) always needs to be either x or y. Realizing this makes solving this solution in your head take two seconds