[AlanHo]

I have been clearing out some old paperwork today and I came across a folder containing some papers from 60 years ago - at the time when I was in 6th form grammar school.

I came across some homework the maths teacher had set. He told us it was an interesting geometry puzzle and challenged us to solve it by the following week.

Only two of us in the class succeeded. (OK OK I'm bragging again)

Any good mathematicians here who would like to have a go......................


There are two ladders in an alley leaning against opposite walls. One ladder is 20 feet long, the other ladder is 16 feet long and the  height above ground where they cross is 7 feet.

How wide is the alley?

[rustynutz]

I got the tape measure out and it was 58mm.....

[Phil №❶]

9.6 feet

[AlanHo]

9.6 feet

Not even close. Try using the Pythagorean Theorem. There are 4 triangles involved.

[FatBoy]

Ahhhh, high school maths.  I'd long forgotten that.

8.8888888 feet?

[Phil №❶]

Wrong again, nothin's changed

[Doggie 1]

Was your grammar school in Birmingham?
I used to go one in Edgbaston.

[The Gonz]

This is a combination of Pythagoras and simultaneous equations. It's way past midnight here after a long night with my cadets but I'll take this to work to do over a coffee and post my attempt this evening. 

[AlanHo]

This is a combination of Pythagoras and simultaneous equations. It's way past midnight here after a long night with my cadets but I'll take this to work to do over a coffee and post my attempt this evening. 

An interesting concept - I await your results with keen interest. No-one has yet got close to the correct answer.

I wonder if anyone has gone looking for two ladders of the right lengths and a tape measure to conduct a practical experiment............

[Seoul-mate]

A tough little question Alan .
I must admit that I do teach high school maths...... however I  haven't seen this particular question before.
I'll also admit to using some old textbooks for a few hints and ideas and I found that using an excel
spreadsheet was a handy way to help solve some of the equations. Kept me up well past my usual bedtime .

(click to show/hide)

Anyway I have the alley at approx. 10.6545 ft wide with the longer ladder reaching about 16.9366 ft up one wall,
while the shorter one reaches about 11.9366 ft up the opposite wall.

[AlanHo]

A tough little question Alan .
I must admit that I do teach high school maths...... however I  haven't seen this particular question before.
I'll also admit to using some old textbooks for a few hints and ideas and I found that using an excel
spreadsheet was a handy way to help solve some of the equations. Kept me up well past my usual bedtime .

(click to show/hide)

Anyway I have the alley at approx. 10.6545 ft wide with the longer ladder reaching about 16.9366 ft up one wall,
while the shorter one reaches about 11.9366 ft up the opposite wall.

Correct - but I had to do it before computers were around (long-hand - so to speak). The nearest we got was an abacus.

Did you make an allowance for the rubber feet on the ladders?   

I will publish my (50 year old) hand-written on papyrus workings later.

[The Gonz]

Damn you, Alan. I ended up still at it with successive approximation using some resolved quadratic-looking equations involving figures 256 and 400 on the bottom lines. I'm going to bed 3 hrs later content that the answer lies on the

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high end of between 10 and 11

. And my successive approximations were all on paper!

[eye30]

Due to the calculator which I found and is circa 140's I had to work in inches.

So after a few attempts decided it was about 127 inches which when these house was built was the minimum, allowable, distance between house.

[The Gonz]

  Come on, even the Americans have mustered up enough intellect - in Star Trek - to go metric.

[AlanHo]

My solution which was done the old fashioned way using awesome brain power and tenacity - without any assistance from a computer (or even a typewriter).

I wonder if 16 year olds could do that today - in the UK I very much doubt it having tried it on 2 otherwise bright grandchildren at university who are studying engineering subjects.

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[Seoul-mate]

My solution which was done the old fashioned way using awesome brain power and tenacity - without any assistance from a computer (or even a typewriter).

I wonder if 16 year olds could do that today - in the UK I very much doubt it having tried it on 2 otherwise bright grandchildren at university who are studying engineering subjects.

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Brilliant solution Alan!
However I did notice one error (circled in red, as all good teachers do).
This was probably a simple transcription error when you re-wrote your
final copy because in the next line it is correct again.

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