## Mathematical diversion: the ladder problem

This is a mathematical diversion to while away some time, and stim-
ulate your brain. Try solving it before looking at the paper, as it states
some basic equations and approaches quickly. The problem is stated be-
low.
There is a vertical wall, and a horizontal floor. A box, measuring 1m
x 1m x 1m lies on the floor, and is flush against the wall and the floor.
The problem is actually in 2D, so you can ignore depth. Suppose there
is a ladder, of length c, which is propped so that the top of the ladder
touches the wall, the bottom touches the floor, and somewhere along its
length it touches the corner of the box. The question is: determine
b, the horizontal distance from the bottom of the box to the point at which the
ladder meets the floor. You may assume c= 3 if that helps. There are no
tricks in the statement of this problem.

Computer programmer living in Scotland.
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### 2 Responses to Mathematical diversion: the ladder problem

1. MrContrarian says:

I used Wolfram Alpha to factor the quartic. I suppose you think that’s cheating but it’s what any workman would do.

• mcturra2000 says:

“I suppose you think that’s cheating”

You bet!

I actually obtained the four roots by using wxMaxima, but that’s OK, because I essentially solved the equations beforehand.

I see Mathematica “Starter” is \$900, and the Standard version is £2240. Ouch! I’m not sure why anyone would buy it when there’s many good free alternatives available.