17 replies to this topic

[Bikerman]

Yes correct answer: well worked out.

[Shahrukh]

Bikerman, on 14 August 2010 - 11:00 PM, said:

Yes correct answer: well worked out.

Thank you.

Answer 3:
h = total hens
p = total pigs

2h + 2p = 60
2h + 4p = 86

60 - 2p = 86 - 4p
2p = 26
p = 13

2h = 60 - 26
2h = 34
h = 17

[Bikerman]

Shahrukh, on 15 August 2010 - 12:27 AM, said:

Thank you.

Answer 3:
h = total hens
p = total pigs

2h + 2p = 60
2h + 4p = 86

60 - 2p = 86 - 4p
2p = 26
p = 13

2h = 60 - 26
2h = 34
h = 17

Yet again correct....applause rings out...
OK as the final one of this series, something a bit more tricky perhaps...

Question 4

In my street, there's only one side with houses. The sum of all the housenumbers smaller than mine is equaly to the sum of all housenumbers bigger than mine. The 'connection/relation' between my housenumber x and all houses in my street is?

[rvalkass]

Bikerman, on 15 August 2010 - 03:27 AM, said:

In my street, there's only one side with houses. The sum of all the housenumbers smaller than mine is equaly to the sum of all housenumbers bigger than mine. The 'connection/relation' between my housenumber x and all houses in my street is?

Is that you're the only house on the street

Sum of all the house numbers smaller than yours = 0
Sum of all the house numbers greater than yours = 0

0 = 0

Q.E.D.

I think this is why my teachers hated me at school

[Bikerman]

rvalkass, on 15 August 2010 - 07:19 AM, said:

Is that you're the only house on the street

Sum of all the house numbers smaller than yours = 0
Sum of all the house numbers greater than yours = 0

0 = 0

Q.E.D.

I think this is why my teachers hated me at school

That could be a solution, but it is a bit trivial :-) There is another less trivial one

[rvalkass]

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]

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 ).

Quote

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 by Bikerman, 15 August 2010 - 09:17 PM.

[Bikerman]

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...