42

One of my pupils this year was Justine.  Her father has unusual and advanced beliefs about his parental responsibilities towards his 10-yearold daughter.  These include – and who would argue against him – ensuring that Justine is thoroughly familiar with that seminal text The Hitchhiker’s Guide To The Galaxy.  Naturally enough, this means that Justine immediately recognises the significance of the number 42 as The Answer To The Ultimate Question Of The Life, The Universe, And Everything.

It seemed only right that I put together some activities for Justine to explore, preferably with her father:

 

In this number pattern what is the value of the third row?

1+2 = 3

4+5+6 = 7+8

9+10+11+12 = 13+14+15

….

Can you continue the sequence?  What can you find out about the pattern?

……………………………………………………………

42 is adjacent to 41 and 43, so it is sandwiched between two prime numbers.  Are there other numbers which are sandwiched between two primes?

……………………………………………………………

42 can be written as the sum of consecutive numbers in these two ways:  9+10+11+12 and 13+14+15.  Are there any other ways of writing 42 as the sum of consecutive numbers?  Can all numbers be written as the sum of consecutive numbers?

……………………………………………………………

10 can be “partitioned” into smaller whole numbers.  For example, 6+3+1 = 10, and  3+2+2+1+1+1 = 10   Can you find all the 42 different ways of partitioning 10?  Go on, have a try!

……………………………………………………………

Here’s a PS – I hope Justine smiled when she tackled this question in the Key Stage 2 Tests a couple of weeks ago ….

2014 P1 Q15

 

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3 responses

  1. This activity was my first time partitioning numbers. I found 41 different partitions for 10 and was stumped trying to find the 42nd until I realized I hadn’t included 10 by itself.

  2. Gosh, that was quick! It took me a day or two and a lot of checking. I was surprised how much persistence I needed, and telling you how many partitions you’re looking for seemed helpful. Of course, it was the 42 aspect that struck me – of course, smaller numbers generate fewer partitions. Good luck!

  3. I let excel help me keep track of the partitions.

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