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?
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.
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.
I'm obviously not as sharp as Steve I may be misreading this - is the interest a factor in the £888? Dave
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?
£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.
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
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?
I don't know if my method is the same as yours, but I did find a simple method using algebra and integer logic.
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.
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.
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'
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.
Very interesting! Like all good ideas, it is simple, but not obvious. Personally, I like to store ideas like this in my brain. You never know when they may prove useful to make a similar task a little easier.