h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

555? Aww, that must be fake!

Anyway, here's mine (I was feeling negative when I worked this out)

-1-7+(-5*5*(5-7))

Is that about right? And fortunately there wasn't SOHCAHTOA in sight.

There are surely some numbers which cannot be reduced to 42 using the operations which we are allowed. Can anyone think of an arithmetical operation which can derive 42 from 100000?

You'd probably have to resort to invtan(1)-0!-0!-0!+0+0 = 42
though invtan feels like a bit too much of a cheat unless its absolutely necessary, and requires youre working in degrees rather than radians. I can't quite see any other way to do it.

Or...you can also recall that in very special circumstances, 6 x 9 = 42, in which case:

(10 - 0!) x ((0! + 0! + 0!)!) = 42

Just thought up an alternative for the notorious U109000 which doesn't use this extreme trick, but gave me the idea:

(-1-0!+9) x ((0! + 0! + 0!)!) = 42

I'm no mathematician, so what's the justification for 0! being 1? After all, if 0! = 1! then 0 = 1, a proof which I remember as the holy grail for the maths nerds at school.

And what's an invtan? I've been wandering the maths dictionaries of the web for half an hour, and I can't find it.

0! = 1! does not imply that 0 = 1, just as (for example) 3^2 = 9 = (-3)^2, but this doesn't mean that 3 = -3

0! is defined to equal 1 for reasons of consistency. I can't really give you a non-mathematical reason why it's defined that way - best I can do is this:

n! is the number of ways of choosing n objects in order, so for example, there are 3! = 6 ways to choose an order for the letters a, b and c:

abc
acb
bac
bca
cab
cba

This works for all n bigger than 0: there are 2 ways to choose an order for 2 objects, and 1 way to choose an order for
one object. Now how many ways are there of choosing an order for 0 objects? Well, maybe you could claim 0 ways, but mathematicians would say 1 way (strictly they would say that the number of permutations (bijections) on a set with no elements is 1).

invtan is the inverse of the tan function. Look up tan and there ought to be a reference to it. Also known as tan^(-1) or arctan.

Thank you HenryS - ably overfilling my Shoes in my enforced absence!!!

I will add you (U175557) to the list of people to add.... Check the page again in a couple of days...

Cool beans! Danke.

I put 109000 = 10 * (sqrt(9) + 0!) + 0! + 0! up ages ago. Obviously someone whose name may or may not end in a number didn't see it .

And since the Guide treats U000013 as the same as U13 you can do ((0! + 0! + 0! + 0)! + 1) * 3!.

U100000 is a little harder. How about R((1 + 0! + 0! + 0! + 0 + 0)!) = R(24) = 42, where R(x) is the well-known Reversethedigits function. Or S(1 + 0! + 0! + 0!, 0! + 0!) = S(4, 2) = 42, where S(x, y) = xy is the equally well-known Stickthemtogether function.

admission - I've never seen that version of the 109000 before.....

So The guide treats U000013 the same as U13 and thus U000281 as U281???

I will check - if so it lets a few people (italics) off the hook!

Only way I can get U100000 to = 42 is using invtan using standard Calculator commands.... But, if we start using Excel functions things'll just start getting silly(er).....

ie if you point your browser at U000013 you end up at the same place as if you point it at U13.

Quite handy

Same with Abi - U000281...