Fun Math Problem 'Cussed Ladders'

[Gerson W. Barbosa]

(09-21-2017 12:20 AM)Mike (Stgt) Wrote:  If you like problems with ladders, here is another one.

Ciao.....Mike

h = '1/2*(√26+√(25-2*√26-2))+1/2' = 4.83850116068 m (to be checked)

[SlideRule]

(09-21-2017 12:20 AM)Mike (Stgt) Wrote:  If you like problems with ladders, here is another one.

"The 'ladder and box' problem is relatively new;
it first appeared in A. Cyril Pearson’s 1907 20th Century Standard Puzzle Book
(London). But its' mathematical underpinnings have been traced back to Nicomedes
(~200 BCE), as well as to Newton (1720) and Thomas Simpson (1745).
The problem ... is just one in a group of 'ladder' problems"

A solution is presented at Shortest Ladder Problem

References:
Pearson, A. C., 1907, 20th Century Standard Puzzle Book. London: George Routledge
& Sons, LTD., New York: E.P. DuMon.

Simpson, T., 1745, A treatise of algebra, reproduction from Cambridge University
Library, London: John Nourse, p. 250.

Wells, D., 1992, The Penguin Book of Curious and Interesting Puzzles, Dover,
p. 130-131, problems 399 and 400.

BEST!
SlideRule

[Gerson W. Barbosa]

(09-21-2017 01:55 AM)SlideRule Wrote:  A solution is presented at Shortest Ladder Problem

I just submitted an easily obtainable equation to W|A and chose the second result. I would’t solve the quartic equation by hand, even if I knew how to do it.

http://m.wolframalpha.com/input/?i=solve...5D%2Cfor+h

Gerson.

[pier4r]

(09-21-2017 01:55 AM)SlideRule Wrote:  "The 'ladder and box' problem is relatively new;
it first appeared in A. Cyril Pearson’s 1907 20th Century Standard Puzzle Book
(London). But its' mathematical underpinnings have been traced back to Nicomedes
(~200 BCE), as well as to Newton (1720) and Thomas Simpson (1745).
The problem ... is just one in a group of 'ladder' problems

A solution is presented at Shortest Ladder Problem

References:
Pearson, A. C., 1907, 20th Century Standard Puzzle Book. London: George Routledge
& Sons, LTD., New York: E.P. DuMon.

Simpson, T., 1745, A treatise of algebra, reproduction from Cambridge University
Library, London: John Nourse, p. 250.

Wells, D., 1992, The Penguin Book of Curious and Interesting Puzzles, Dover,
p. 130-131, problems 399 and 400.

BEST!
SlideRule

Thanks for sharing!

[Gamo]

Thank You to pier4r

You explanation is very clear

Gamo

[SlideRule]

(09-26-2017 12:36 AM)Mike (Stgt) Wrote:  

(09-21-2017 01:55 AM)SlideRule Wrote:  A solution is presented at Shortest Ladder Problem

One question ... How may I set (making?) C when the solution shown computes C?

Consider C as the independent variable and then compute the size of the corresponding box? Since I didn't create the referenced solution, I interpret the quoted extract as just such a 'reverse' engineering' proposal.

BEST!
SlideRule