What is the benefit of doing "trial and improvement" with a
spreadsheet, when a calculator is often faster and more convenient?
Well firstly, I'm all in favour of calculators, and I certainly
prefer quick answers to long methods.
But sometimes I need to see the things I've already tried, before I
have another go, and that's where a spreadsheet helps.
So here's the puzzle:
Find a fraction a/b that is as near as possible to 0.46291
That's simple enough: 46291/100000 does it exactly.
And since 46291 and 100000 don't share any factors that's also the
simplest version of the fraction.
Now try to find new a and b values, where a and b must each be less
Here's my start at this on a spreadsheet. I've put my guesses in
columns A and B, and let the spreadsheet do the division.
Now it's your turn. Click here
to get the Target
Decimal Excel file.
(Standard click-select will open the file, but to download it to
your own machine: right-click on the link, and choose Save Target
As . . . )
Change my choices if you like. Add three more attempts. What was
How would you explain your strategy so that someone else could use
it on a new target decimal value?
Compare your approach with the strategies of other people working
on the task.
Change the rules
- How about a and b values both under 40?
- What about, instead of division, multiplying a and b to get as
near as possible to 789?
For the original a/b challenge, devise a scoring system that
favours the player who:
- takes least goes
- gets closest to the target
- and uses the smallest values for a and b.
How could you decide whether your system was fair?
Compare yours with someone else's system. How do you decide which
system is fairer?