Math Is Fun Forum

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Edna's age

Edna is as old as Henry will be when Edna is twice as old as Henry was when Edna's age was half the sum of their present ages.

Henry is as old as Edna was when Henry was half the age he will be 10 years hence.

How old is Edna?

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Edna's age

Henry is 2 years old and Edna is 6 years old.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Edna's age

Henry is 2 years old and Edna is 6 years old.

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."

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Edna's age

Last edited by 1a2b3c2212 (2009-08-19 01:27:24)

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Edna's age

Hi 1a2b3c2212,

"so confusing". Yes...good for giving one an eye-ache!

Sorry again, but both those equations are incorrect. Understanding the puzzle's logic is at least as difficult as working out a solution strategy!

And if you want a really good headache, try the "Self-Referential Aptitude Test" puzzle I posted about 5 weeks ago (it's just about to fall off page 1 on this forum). It's just a logic puzzle...but very testing!!

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: Edna's age

I like this kind of puzzle. I find that the best way to make any sense of sentences like these is to read them from right to left.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Edna's age

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...:(

Last edited by phrontister (2009-08-19 10:10:42)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Edna's age

Here are the equations for the algebraic solution I mentioned in my previous post:

Excel spreadsheet image below (for the solution, just change Edna's bogus age in D11 as per the yellow highlighted instruction). Goal Seek aid included.

The formulas in column E were copied from the coloured cells to their left...ie, from columns C & D. Simply type them into those coloured cells to get your spreadsheet to run.

Btw, I used Conditional Formatting to change the fill colour in C20 to green once a correct solution is found...and "WRONG!" changes to "SOLVED!" because of the formula.

Just ignore the second image, as it's replaced by the first. It's playing stubborn and refuses to be deleted.

Last edited by phrontister (2009-09-14 13:24:06)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Edna's age

Hi phrontister;

Checked your simultaneous equations in algebra. Good Solution!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Edna's age

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.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: Edna's age

From the first sentence one can get..

from the second sentence one can get..

where E and H are Edna's and Henry's current ages respectively.
solve for one and substitute in the other for the answer.
Thanks phrontister! Good confusing problem.

Last edited by Fruityloop (2009-08-31 15:56:49)

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Edna's age

Terrific solution, Fruityloop! Thanks!

I hadn't thought of trying that. Very neat and concise!

It lines up pretty much with my spreadsheet solution, in which I linked the two sentences by calling upon the same age-difference cells.

I've made some minor changes to my spreadsheet solution in post #8 to make it a bit clearer, and for some small corrections. Just ignore the second image - it won't delete for some reason (I've posted about that in the Suggestions and Comments forum).

Last edited by phrontister (2009-09-14 13:28:14)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson