Solve the Credit Crunch

Discussion in 'Math' started by studiot, Apr 18, 2009.

1. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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One year after the British Prime Minister's wife had a new baby on his birthday, the Chancellor announced.

This will solve the Credit Crunch.

If I deposit the number of taxpounds equal to the product of your age and your child's age, and do this every year from now on, this will accumulate a useful fund to squander in the future.

After a few years the PM asked the Chancellor "How much have I got to squander".
I don't know exactly, replied the Chancellor, because there has been some interest, but I have deposited £888 in total.

How old was the Prime Minister when the child was born?

2. steveb Senior Member

Jul 3, 2008
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I came up with an age of sqrt(sqrt(130321)). I express it this way so as not to give the answer away to anyone trying to solve.

3. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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These are obviously too easy for some folks.
Perhaps you should be Chancellor?

4. steveb Senior Member

Jul 3, 2008
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No thank you. Our econonic woes are beyond my feeble skills!

Problems like this can be solved with a computer fairly quickly, but I always look for an "on-paper" approach. There is a nice simple way to solve this one.

5. Dave Retired Moderator

Nov 17, 2003
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I'm obviously not as sharp as Steve

I may be misreading this - is the interest a factor in the £888?

Dave

6. steveb Senior Member

Jul 3, 2008
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I assumed the interest was not a factor.

I thought I should mention that there is a trivial solution of the PM age equal to 887, but this is eliminated since the PM is not a biblical figure. Also, it is mentioned that the deposits were made for a few years, not one year.

Also, I was wondering of there is a minimum age requirement to be the British PM. An age of 19 seems too young, but perhaps there is no law against that?

7. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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£888 was the total deposited by adding together the amounts deposited each year. Interest was not a factor. (I could have made it more realistic at £888 billion). It is also relevant to assume the PM to be older than 12.

8. Dave Retired Moderator

Nov 17, 2003
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I am quite sure our current PM would contest your assertion of not being a biblical figure. Comparisons he has made of himself thus far are Churchill, Roosevelt, Heathcliffe from Wuthering Heights, and Titian. A biblical character doesn't seem that unlikely does it!

In theory you could be PM at 18 because the age at which you can become an MP is 18 as amended by the Electoral Administration Act 2006. We don't elect a PM, we elect MPs and the largest party selects the PM from their party's MPs.

Ok, thanks. I will have a sit down with it later, I must confess it is not completely obvious at this stage (though I bet its easy when you know how).

Dave

9. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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As Steve says,
You can start a 1 and get a computer to try every possibility (there aren't reeally that many ) until you get a hit.

But there is an algebraic method. It's not a simple formula though you have to use a bit of nouce with it as well.
Did you ever get this method as well Steve?

10. steveb Senior Member

Jul 3, 2008
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I don't know if my method is the same as yours, but I did find a simple method using algebra and integer logic.

11. maison09 New Member

Apr 23, 2009
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Thank you so much for your sharing

12. steveb Senior Member

Jul 3, 2008
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Now I feel guilty for not sharing the solution. There didn't seem to be much interest in this one, so I didn't post it. The attached PDF shows my approach. I expect there are other methods.

File size:
17.7 KB
Views:
23
13. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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A nice piece of deduction and algebra, Steve.

Yes there are other approaches, but so far as I know, they all boil down to realising the

2^4*3^2*37 step and the consecutive integer requirement.

14. steveb Senior Member

Jul 3, 2008
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Thanks! Nice problem by the way. Did you invent it?

15. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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No can't claim the credit for it.

I think the last mathematical thing I genuinely invented was something published in the 'Empire Survey Review' back in 1986, which I entitled

'The use of the fifth quadrant'

16. steveb Senior Member

Jul 3, 2008
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That title is too intriguing. Can you explain the gist of this idea?

17. studiot Thread Starter AAC Fanatic!

Nov 9, 2007
5,005
515
Surveyors and navigators measure bearings (angles) clockwise from North (y axis) Mathematicians and engineers measure them anticlockwise from East (x axis).

Programs for calculators and computers were written by mathematicians so use the mathematical convention.

Whichever convention is used, there is much room for sign convention confusion and error. And in programming it is necessary to make logical tests and decisions to calculate over the whole circle traced out by the rotating arm when calculating x and y components.

My method provides a single do-it-all formula.