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.

To read the full article (which has mathy stuff in it so I can’t type it here): http://pdf.markcarter.me.uk/ladder.pdf

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

“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.