**Question 4: If a=9, b=30 and c=25, what does x equal?**

Part of me just wants to say 42.

But despite the inherent sci-fi coolness of that answer, it might be cheating.

Also, I have a cleverer theory, and it goes something like this:

- For any given string of numbers, however random, you should be able to construct a triangle of differences.
- First off, the numbers themselves are 9, 30 and 25.
- Therefore, the differences between consecutive numbers in the sequence are 21 and -5.
- Therefore, the difference between the differences is -26.
- So we now have a triangle, like so:

9 30 25

21 -5

-26

- If each row is extrapolated towards the right, assuming the difference between the differences is a constant -26, we get something like this:

9 30 25 -6 -63 -146 ...

21 -5 -31 -57 -83 ...

-26 -26 -26 -26 ...

- Assuming
*a*to be the first number,*b*to be the second and*c*to be the third, it seems logical to say that*x*must be the 24th, since it is the 24th letter of the alphabet. *x*, i.e. the 24th value in a sequence which begins with 9 and has a difference between differences of -26- And if this line of logic is followed far enough, you can determine the value of the
*n*th number in the sequence, for any*n*. - I think the formula works out as...
**insert a longish pause while I try and fail to boil all those numbers down to a simple equation**- Well, what I've got so far is "
*n*(*x*) = (*n*(2) -*n*(1) ) + ", which isn't even a complete equation, and I'm pretty sure it would still be wrong even if I'd bothered to finish it. - Stuff this for a lark; I'm going to fire up Excel and get it to calculate
*x*for me! - My helpful spreadsheet program tells me that the 24th number in this sequence, i.e.
*x*, is -6086. *x*must therefore be -6086. Because Microsoft Excel 2007 says so.- Tada!

Okay, that was arcane.

Perhaps I should have settled for '42'?

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- The Colclough

I must confess that your answer is far more interesting than the one I was thinking of, and you found it in a far more interesting way. So the points go to you. However, the actual value of x that I had been thinking of was -5/3. A classic formula that uses the terms a, b, c, and x is a quadratic formula. A quadratic formula is in the form ax^2+bx+c=0, thus is in instance the formula is 9x^2+30x+25=0. To find if x has more than one solution, use the quadratic formula: -b/2a +or- sqr root of b^2-4ac. Which happens to work out as 30/18 +or- sqr root of 0/18. That proves there is only one answer for x. Factorising the equation give (3x+5)^2=0. Divide both sides by themselves, and you get 3x+5=0. That can be rearranged as 3x=-5. Divide by 3 to get x on it's own... x=-5/3.

ReplyDeletei did know that stuff once. but i never enjoyed it at the time and i've been happily forgetting all about it ever since finishing my maths GCSE, which was... *counts slowly* about 8 years ago, so i'm not surprised i didn't cotton on to the quadratic possibilities.

DeleteMy Brain Hurts.

ReplyDeletecondolences. mine didn't feel to great by the time i'd finished writing this post either.

DeleteIt took almost 8 attempts to post that comment, is there an easier way?

ReplyDeletenot that i'm aware of.

Delete