[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 273
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390625 = 5^8 and there is a zero inside. Terver has nothing to do with it.
And remember, I suppose, that there will always be 25 on the end.
P.S. The problem is for 8th-9th grades, and I haven't got a single good idea how to solve it yet...
I don't know about intuition, but the number you wrote doesn't prove it in any way.
What number are you talking about?
Apologies. Celebrating the holiday - misread the condition. All erased.
I'm going to hypothesize that it is this number 5^1000 itself.
By the way, Swetten, happy holidays to you :)
Another hypothesis is that the number is periodic, like ......(625) and therefore has no zeros in it.
There is another hypothesis: if there is a number A of n digits (without zeros), which is divisible by 5^n, then to this number you can add a digit b to the left (of course, non-zero), so that the resulting bA is divisible by 5^(n+1). I guess by induction it is possible somehow.
The number 5 is apparently there for a reason. Why 5? What is the power of 1000 for? So that it is impossible to calculate neither on a calculator, nor in ordinary programs on a computer. Perhaps it is not necessary to take such a large degree and "technique works" at smaller degrees.
That's right, that's why they make these problems for poor schoolchildren. They don't even give them calculators. They're being completely mocked.
They're being bullied to the max.
That's why they go to school:) Well, they don't go there for a paycheck:)
I remember they didn't even give us calculators, we used to count the sines on a 4-digit Bradis table:) I wonder if they use them now.
Probably yes, although I'm not 100 per cent sure. The calculator might break (or the battery might die). What if the sine or logarithm still needs to be counted?
Here's another problem I just made up myself:
How many digits in 2^1000?
You've only been given paper and a pen. No Bradis tables, logarithmic rulers, calculators and other wonders of the scribble age.