For Those Who Want A Brain Work Out.......nice Little Maths Problem ...No Calculatiors

[ToraToraTora]

X²³ = 27368747340080916343    

Solve for X

No calculator, show your workings.....

[newmodarmy]

well it's going to be more than 2 as I doubled it 23 times (with some rounding) in my head and only got to 8 million.

And it's got to be less than 10

[barry1010]

x= 3.14

Take the 23rd root of both sides:

[ X = \sqrt[23]{27368747340080916343} ] =

 X \approx 3.141592653589793 ]

 

 

[ToraToraTora]

X is an integer if that helps

You need a calculator to take roots like that barry.

[newmodarmy]

ah- the clue is in the last 3 digits!

[Etch]

As newmodarmy says, the answer has to be less than 10 (10²³ has 24 digits, which is larger than the right hand side). X can't be even because the RHS ends in an odd number, so not 2, 4, 6 or 8. It can't be a multiple of 3 because the digits don't sum to a multiple of 3, so not 3 or 9. Can't be 5 because the last digit isn't a 5. Which leaves 7.

[ToraToraTora]

yes etch BA, looks impossible without a calculator but a little deductive reasoning and the answer pops out.

[barry1010]

I was testing the powers of AI, not using a calculator.  

[ToraToraTora]

well whatever you were doing Barry you were miles off.

[barry1010]

It wasn't me, guv

[THECORBYLOON]

There are twenty digits in the number which is less that the power.

For large powers, the number of digits exceed the power when the original number is higher than seven.

The resultant number is odd so the original number must be three, five or seven.

It doesn't end in five or zero so the original number cannot be five which leaves three or seven.

When multiplying three by itself eight times, it has only four digits meaning there will be fewer than twenty if the power is twenty-three.

That means X must be seven.

 

[Prudie]

Interesting that the powers of AI came up with the accepted approximation of π

[ToraToraTora]

13:05 there is no such thing as AI, the most wrongly named thing in history. Gawd knows what barry was doing but the answer that etch gave is correct.

[Prudie]

I think you've missed my sarcasm