Math Is Fun Forum

Hi Bobby,

You got it!

What method did you use?

I'm just starting to type out a method that basically follows the spreadsheet one, but expresses it differently. I'll post it soon.

They're good!

I also reckon that before anyone gets to X-out the first 5 words listed there they'd have Xed-out a full 5-by-5 grid just filled with "in terms of"...a good escape clause by which one can avoid having to think about how to properly phrase their exact intention.

Good for politicians, media presenters, lecturers...and such-like, etc, and so forth, and so fifth.

Hi Bobby,

Thanks!

I've got another one of these that can be solved in much the same way (algebra and spreadsheet). I'll post it later on today.

Hi Avon,

You're quite right! And I use that right-to-left strategy too.

I have a spreadsheet (Excel) solution that I'll post an image of when I get home from work.

I've included formulas and explanations in it, and also an option for using Goal Seek.

I also have an algebraic solution that I'll post too.

Glad you liked it. I've got a couple more of these that I'll post later. One's a new one that I found yesterday and haven't tackled yet, and I'd like to solve it first before posting.

Gotta rush...:(

Impossible! The horse would have to be 840 feet wide! See my reasoning in post #6 re the single-lap scenario.

Hi Bobby,

It maintains a consistent increase in the distance difference.

To achieve that 1-mile hoof difference over 30.5 miles (centre of horse's torso), would travelling in a spiral give the same result as for travelling in circles? Too hard for me.

Sorry, 1a2b3c2212, but that is incorrect.

If Henry is 2 now, in 10 years' time he will be 12. Half of 12 is 6 - which is older than he is now - and so that doesn't agree with the tense of "was half the age he will be 10 years hence."

Hi Bobby,

I used Janet's (LibertyBasic) program from shiwaji's "Sum of fractions which equals 1" thread - with some adjustments for your problem - and it found only the solutions you posted above.

Hi 1a2b3c2212,

You got it...nice!

I've just got a couple of comments about your answers to the bonus questions:

Hi 1a2b3c2212,

Ah...thanks for that. You rescued me from trying to draw the solution in a series of steps, which wouldn't have been easy!

Your time of 2 min 02 sec is pretty impressive! Is that just for the physical crossing bit, or did that also include working out the strategy? If it's both, that sounds mighty incredible!!

Hi 1a2b3c2212,

If the max number of persons on a plank at any one time is 6, then I reckon the minimum number of plank placements is as per my drawing B (ie, 11).

I'd split the 13 people into 2 groups of 6 + a single. So that the max limit of 6 per plank isn't exceeded, people from those groups, and the single, would at times have to occupy stepping stones (also occupied by one end of a plank) while the planks are moved into position (only one person per stepping stone is allowed, I presume). The planks would be passed from one person to the next as best suits the occasion and positioned in the order shown in the drawing.

I think the foremost planks and stepping stones should be populated as soon as possible.

I kept the Word file for my drawing B and moved objects around to find the optimum strategy, but I don't think I could illustrate that well in a single drawing...I'd have to do a series of them.

I take it that doesn't include the part of a plank that rests on a stepping stone or another plank, otherwise I'm pretty sure it can't be done.

Hi Bobby,

Yes - I'll have to remember that for situations where that is important (or maybe I should make it a habit anyway).

Some day this quirk won't exist and we won't have to dream up workarounds...and we'll laugh at the clunky ways of the old days.