Stage: 2 and 3 Challenge Level:
Tom Kimber, a teacher at Westdene Primary School in Brighton emailed us to say:
I am a MaST teacher who was lucky enough to be at one of your recent NRICH events in London. I got into a really interesting mathematical discussion with some very advanced pupils in my class about the pattern of the units column in numbers-to-the-power-of.
Anyway, after a long and convoluted journey through many different mathematical areas, it has reached a concluding* question. I thought I'd share it with you as my children have ENJOYED getting their teeth into it:
Look at this calculation:
$7^x + 9^y =$
I get a random number generator to generate two random whole numbers. The first one it generates I place in position $x$. The second number it generates I put at position $y$. What is the probability that, when I complete the calculation $7^x + 9^y =$, I will get a number that is a multiple of $10$ as my answer?
Hope you find it as interesting as we are!
* - I say concluding... probably not!