- it ends in 3, so the cube root must be a multiple of 3
- 30*3 is intuitively going to be 27,000, and 20*3 will be 8,000
- that leaves only 21, 24 and 27 to choose from, and given the exponential shape for 8k - 27k, I went with the largest
Not a "solution", as I couldn't be certain without confirming, but interesting how close a logical deduction could get.
Intuition is incredibly underrated - I have learned to trust the first damned fool thing that pops into my head, before any conscious thought has had time to get moving and therefore interfere. It’s usually correct, regardless of context - and when it goes wrong, it’s because I accidentally allowed myself to think and reason.
It’s in the same category as “walking away from a problem”, in my view - you can’t solve it, you go grab a coffee, and while you’re looking for the sugar the answer is just suddenly there in your head, because you stopped running the CPU-intensive conscious process, and let the background workers catch up.
Conscious thought is great for producing outputs for other humans to then work with. Unconscious through this great for… everything else. We do incredibly complex things all the time - catching a ball, walking upright, looking in the direction of that sudden sound - but typically run all of the gnarly logic in an abstraction layer within a virtual machine, rather than on the hardware that was designed to run it natively.
No end of trouble at school where I wouldn’t just not show my working, but couldn’t - but the real world fortunately doesn’t particularly care about the means, just the ends.
I doubt the average person can rely on their untrained intuition for large square roots.
One of my favourite tricks is just knowing, to +- 1 minute, what time it is. I don’t set an alarm, I just plan to wake at whatever time. If someone asks the time I give it without checking. It actually works better when I’m asleep, as I will wake +- 10 seconds from the intended time, which shows just how much consciousness interferes.
Honestly, it’s laziness - thinking takes far too much effort and is much too slow, and 80% right in 1% of the execution time is a “good enough” optimisation.
The "cube root" part contains the implicit information that we have a product ending in 3, of three identical factors.
I guess the missing assumption is that given the context of solving the cube root in ones head, it would more likely be a trick that only works with integers, and as such the correct answer might be expected to be one.
I don't get it. 7 cubed is 343. The article explains better what numbers might have cubes ending in 3.
37*3 also ends in 3 but is not divisible by 3. Thus, were the range not capped at 30 it may have been illegitimately discarded by the criteria.
I think the 3 combined with the 5 digits and 20-30 range, made my guess a bit lucky. It's also contrived for that cube, so not useful for others, other than perhaps as a direction to go in (and likely arrive at the article).
Since it's too small for the cube root to be 57, 27 is the answer.
> - it ends in 3, so the cube root must be a multiple of 3
And also believe this > that leaves only 21, 24 and 27 to choose from,
without noticing that 21^3 ends in 1 and 24^3 is even?
It's like you're doing math in a while different axiom system.
But not notice that this >
I was doing math in an axiom system made for the problem.
Possibly not a good idea in math, but in programming it's kind of what we do. (I don't guarantee it's bug-free or works with different input...)