19 November 2013

Interesting unintended consequences. And a puzzle.

Part of an email I got from my good old friend Jyotsna from Singapore:

“Btw your puzzle format on FB was an inspiration to the math teachers at the boy’s school. I had asked the teachers to look at posting puzzles in a forum so that kids can help out each other and gave your puzzles discussion as an example. It is the second week of this discussion on the school forum and the class kids seem to love it!! So you are pretty influential in far away Singapore! :-)”

What started as an exercise to get rid of boredom on a flight back from DC a few years back has certainly had some unintentional – but highly welcome 🙂 – consequences. Thank you Jyotsna!

This puts pressure on me to post the next puzzle. This one is dedicated to the kids in Singapore and elsewhere. And also adults.

(Again, do not post in Comment section; send me FB msg; I will respond)

A few days back, I was cleaning my pool and talking to my another good friend Kuntal over the phone. He had posed a question – “what is the last digit of 19^19 + 99^99”. Over the phone we discussed our answers – he had taken an elegant way to solve it – I had used a short cut.

So let’s try that:

1. What is the last digit of the sum of 19 to the power of 19 added to 99 to the power of 99. (19^19 + 99^99).
And an extension..
2. What is the last digit of
9^9 + 19^19 + 29^29 + 39^39 +……+ 99^99

3. If you have an younger kid – or you are stuck yourself – try with the following simpler version – and then the above two become easier. What is the last digit of 99^99?

Posted November 19, 2013 by Rajib Roy in category "Puzzles


  1. By Rajib Roy on

    Sameer, Arunima, Debatri and Bijetri got the correct answer. As did Neal but I think that was due to two calculation mistakes! Finally two wrongs made a right!!!

  2. By Rajib Roy on

    The answer: if you think about 9 multiplied by 9, it ends with 1. If you multiply 9 any number ending with 1, the last digit is 9. And the cycle continues. Any number ending with 9 raised to an even number is going to end with 1 and raised to an odd number is going to end with 9. Thus 19^19 will end with 9. As will 29^29 and 39^39 and so on.
    So first answer is something ending with 9 added to something else ending with 9 will always give a number ending with 8.
    The second answer – you have 10 numbers all ending with 9. By default it will have to end with 0

  3. Pingback: Puzzles in a Singapore class – Rajib Roy

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