UKC

New Scientist Enigma

New Topic
This topic has been archived, and won't accept reply postings.
 lowersharpnose 06 Jan 2014
The New Scientist Enigma puzzles have been terminated, which is a shame.

I enjoyed this one recently:

A national charity is doing a lottery, tickets numbered sequentially starting at 1. Winning tickets are those where the number is a perfect power (an integer raised to an integer power), like, 1, 4, 343 2048 etc.

With a payout chance of 1%, how many tickets are printed?

I wrote a program to get an answer, interested to know if anyone agrees with my round-number answer (happy to give, just don't want to spoil it).
 Trevers 06 Jan 2014
In reply to lowersharpnose:

I don't follow from the description- If we can raise to the power of 1, then every number is a perfect power. I'd guess it's x^y where x >= 1 and y > 1 but it's not clear.
In reply to Trevers:

Powers > 1. I missed that detail.
 Paul Robertson 06 Jan 2014
In reply to lowersharpnose:

Is it meant to be done with pencil and paper? The algebra is too difficult for me.
I expect the answer to be a bit over 10000 and to end with two zeros
In reply to Paul Robertson:

I had to write a few lines of code.
 Robert Durran 06 Jan 2014
In reply to lowersharpnose:

I think it's 15000.

Some maths, paper and pencil and a calculator.
I doubt a particularly elegant method is possible (used a bit of trial and improvement)
In reply to Robert Durran:

I got 15000 too. I used a program to come up with a list of perfect powers.

150 perfect powers is a lot to do by hand.
 Robert Durran 06 Jan 2014
In reply to lowersharpnose:

> I got 15000 too.

I expect we're both right then!

> I used a program to come up with a list of perfect powers.

> 150 perfect powers is a lot to do by hand.

But you can for, example, count cube numbers up to 15000 by taking the cube root of 15000 and rounding down. I started with 10000 and used trial and improvement (not too arduous). the subtlety is that sixth powers,for example, are also squares and cubes, so you have to be careful not to count them more than once.

 Robert Durran 06 Jan 2014
In reply to Paul Robertson:

So what's the other puzzle you mentioned in the post you deleted?!(I was planning to go out for a run once I'd done the OP's one but it's horrible outside now.....)
In reply to Robert Durran:

Very neat.
 Hairy Pete 06 Jan 2014
In reply to lowersharpnose: If you like that sort of thing; are you aware of

http://projecteuler.net/problems
In reply to Hairy Pete:

I was not aware of that, looks good, thanks.
 Robert Durran 06 Jan 2014
In reply to Hairy Pete:

> If you like that sort of thing; are you aware of

> http://projecteuler.net/problems

That's great; enough for years of fun! They mostly seem properly tricky though.......
Shearwater 06 Jan 2014
In reply to Robert Durran:

> That's great; enough for years of fun! They mostly seem properly tricky though.......

The first 100 aren't too awful, given a bit of thought. Look at the number of people who've completed each problem... fewer than 10000 means it is a pretty hard one, and fewer than 1000 means it is totally unreasonable
In reply to Hairy Pete:

That is dangerous. Have done the first 10 and I should go to bed now.
New Topic
This topic has been archived, and won't accept reply postings.
Loading Notifications...