Maths Problems Thread

[Roflcopter]

#7

Spoiler

x = 35. Found by putting 1+2+...+x-1 = x(x-1)/2 = 49*50/2 - x(x+1)/2 = x+1 + x+2 + ... +49.

#8

Spoiler

There are 250/25+1 = 11 rungs. For the rung length numbering from the bottom, we get L(n) = 45 - (n-1)k with L(11) = 45 - 10k = 25 which implies k=2. So the length of wood required for rungs is 385cm by summing L(j) for j=1..11 (can be done by arithmetic progressions).