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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Another "How old am I?" puzzle like the one for Edna's age that I posted a couple of days ago:

Rita is twice as old as Ann will be when Rita is half as old as Ann will be when Ann is 3 times as old as Rita was when Rita was 6 times as old as Ann.

The sum of the ages of Rita and Ann is 44.

What is Rita's age?

*Last edited by phrontister (2009-08-21 01:23:03)*

"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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

If I got this right then I have a different method.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

bobbym wrote:

Hi phrontister;

If I got this right then I have a different method.

Sorry, but that can't work because:

"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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

Absolutely right! The method I am using only yields 2 possible choices and I managed to pick the wrong one. Sorry to probe around like this but If I don't have the right answer this time I will have to scrap my entire idea. So please bear with me.

*Last edited by bobbym (2009-08-21 15:17:35)*

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

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.

"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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

Basically it worked like this and I think it's just for this problem. The last clue that Rita was at one time 6 times as old as Ann gives these possibilities:

Age of Ann Age of Rita Difference in age now

1 6 5

2 12 10

3 18 15

4 24 20

5 30 25

6 36 30

7 42 35

What the chart says is that only when Ann was 1 to 7 could Rita have been 6 times older. Now if we say that A= Anns age now then Rita's age is one of these:

A+(A+5) =44 A = 19.5 impossible.

A+(A+10) =44 A = 17 and Ritas age is 27 (impossible 27 is odd))

A+(A+15) =44 A = 14.5 impossible

A+(A+20) =44 A = 12 Rita's is 32 Hooray!

A+(A+25) =44 A = 9.5 impossible

A+(A+30) =44 A = 7 Rita's is 37 (impossible 37 is odd)

A+(A+35) =44 A = 4.5 impossible

So only using 2 clues I can reduce this down to 2 answers. So this method is not as good as yours.

*Last edited by bobbym (2009-08-21 17:55:26)*

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

Thanks for providing that!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Thanks, Bobby. I see what you did...logic & eliminations. Btw, you didn't mark Rita = 37 as impossible (not even) on your worksheet.

Here are solution strategies like the ones I posted for Edna's age puzzle:

Excel spreadsheet image below (just change Ann's bogus age in C10 as per E10's instruction). Goal Seek aid included.

*Last edited by phrontister (2009-09-01 04:12:08)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

Thanks for the additional work. I wasn't able to eliminate 37 with my method. It just isn't strong enough to get but 1 solution.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

I wasn't able to eliminate 37 with my method

37 is eliminated because it's odd, not even (same as for 27).

Thanks for the additional work.

I think I like the algebraic approach best. Spreadsheet is good too...like getting a program to run successfully. And Goal Seek is nice - seeing the numbers spin around until the solution is found, and watching "WRONG!" change to "SOLVED!". Pardon my delight...my efforts don't always work out so well!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

37 is eliminated because it's odd, not even (same as for 27).

Sorry, that's the second time I made the same stupid error. I have adjusted the post and thanks for spotting it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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