Some Maths Teasers Maths problems to keep your hand in

[rvalkass 5]

Fine, if I must actually make use of maths

 

Let the total number of houses on the street = N

Your house number = x

 

Sum of all the house numbers lower than yours, S_low = 1/2 * (x-1) * x

Sum of all the house numbers higher than yours, S_high = 1/2 * (N-x) * (N+x+1)

 

To satisfy the question S_low = S_high

x(x-1) = (N-x)(N+x+1)

x²-x = N² + N - x² - x

2x² = N² - N

x = sqrt(1/2 * (N² + N))

 

So, if there are 42 houses on the road, you'd be number 30. Of course this should really be limited to the case where whole integer values of x are solutions, as few people number their house 30.05. This also assumes the houses are numbered in the sequence 1, 2, 3... rather than you living on the odd or even side of the street, houses having been demolished or converted since original construction, and general screwups by Royal Mail.

[Bikerman 2]

Neatly done. It took me two attempts (I couldn't remember the expression for the sum of numbers < n and had to work it out from basics. I worked it out for 0<n<N OK then I stupidly forgot to subtract the 1 when doing the problem - dumbass - I only saw the error when I crunched it - still, got it right the second time ).

Of course this should really be limited to the case where whole integer values of x are solutions, as few people number their house 30.05. This also assumes the houses are numbered in the sequence 1, 2, 3... rather than you living on the odd or even side of the street, houses having been demolished or converted since original construction, and general screwups by Royal Mail.

Typical physicist - always the specific case and never the general solution. No rigour at all....bleedin atom smashers...

Edited August 15, 2010 by Bikerman (see edit history)

[Bikerman 2]

Here are some interesting problems of a more philosophical nature.

* Link 1
* Link 2

I normally rate myself as pretty good but some of the questions caught me out fair and square...