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Father of the Brides

Math brain teasers require computations to solve.

 

Puzzle ID:#8868
Fun:*** (2.35)
Difficulty:*** (3)
Category:Math
Submitted By:dewtell*us******
Corrected By:cinnamon30

 

 

 



The wedding reception was winding down as Bill Johnson, the father of the bride, held forth to anyone who was left to hear his report on the fiscal damages.

"That's the last one married off - thank goodness! That's been one wedding a year for the last four years I've had to pay for. Alice got married three years ago, then Barbara, Cheryl, and now Denise. They've all gotten married on the same day, June 30th, for some reason, and each girl had to have her three sisters as the bridesmaids, but could they share a color scheme? No - each one had to have her own colors. God forbid they should be able to reuse the bridesmaids' dresses, let alone share a wedding dress. Alice tried to persuade Denise to reuse her color scheme, but Denise said she had lived with her older sister's hand-me-downs long enough.

Funny thing, though - each bride managed to get married when her age was just the same as the sum of the digits of the ages of her three sisters. You don't see that every day, I bet. But why couldn't they share something that costs money instead of this trivia?"

Bill didn't mention how old his daughters are, but he's given us enough information to work out all four ages. How old are they?

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Comments

angie*
Dec 15, 2002

I thought you meant the numbers themselves like 21.
dewtell*us*
Dec 16, 2002

I hope it's clearer now. This one is
harder than "Math Reunion" because of the extra
person, but the general solution approach I outline is the same.
I had fun trying to come up with a puzzle where the
key years would all be consecutive. Enjoy!
SPRITEBABE44*
Dec 29, 2002

wow g8t teser bit of a conplicated answer at the end!!!
Codammanus
Apr 27, 2003

And they say MY solutions are complicated. WTG
saska
Mar 07, 2017

Thanks for your puzzle.

I managed to solve it with glpsol (a free linear and mixed integer programming solver, available for most platforms). I uploaded the model file that I used to pastebin for anyone who might be interested to play with it. http://pastebin.com/WsYpVQ7B
dewtell*us*
Mar 08, 2017

Hi, saska. Glad you liked the puzzle. You can also take a look at my puzzle "Math Reunion", which is a similar idea, but with only 3 individuals instead of 4.

I'm not familiar with glpsol, but I've used lp_solve (a MILP solver) and z3 (a general constraint solver), both of which are free. I took a look at your model file, and I think you have a bug, if I understand the code correctly. When calculating the sum of the digits for this year (for example), you need to subtract 9 if the original one's digit was 7, 8, or 9, not just 7. I think your code worked despite the bug because the only woman with an original one's digit of 8 or 9 was Denise, and she isn't contributing to the sum this year.

Thanks for the update. It's good to see that people are still appreciating this puzzle years after I created it.
saska
Mar 27, 2017

> take a look at my puzzle "Math Reunion", which is a similar idea, but with only 3
individuals instead of 4
I will, it should be easier.

> I took a look at your model file, and I think you have a bug
You were right, thanks. Fixed it.

Using the fixed model yielded another possible solution:
Alice is 27, Barbara is 28, Cheryl is 29 and Denise is 30

A B C D
3-years ago: 24 25 26 27 sum of digits(25 26 27)=24 Alice's age
2-years ago: 25 26 27 28 sum of digits(25 27 2=26 Barbara's age
1-year ago: 26 27 28 29 sum of digits(26 27 29)=28 Cheryl's age
0-years ago: 27 28 29 30 sum of digits(27 28 29)=30 Denise's age


Thanks again for all the fun.
saska
Mar 27, 2017

Most of the formatting in my previous comment seems to have been gone. Please note that the little icon in it is actually the digit 8 followed by a right parenthesis.
dewtell*us*
Mar 27, 2017

Remember that Alice is supposed to be Denise's older sister, which I added to the puzzle specifically to rule out that second solution. That needs to be part of the constraints.
saska
Mar 28, 2017

> Alice is supposed to be Denise's older sister

You are right. I missed that. After adding the extra constraint, the model has exactly one solution.

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