don steward
mathematics teaching 10 ~ 16

Wednesday, 22 December 2010


this problem first appeared (as far as I'm aware) in one of Brian Bolt's books*
it's promoted a keen interest in getting from 1 to the highest number
but it's daunting to check repeatedly...

the task is to try to be able to make all numbers from 1 up to as high a number as you can.

you put any six numbers in the regions (there could be repeats)

you can only add up numbers in regions that are adjacent (have a common border)

you can only add in a number from a region once

for example, if 18 is in the middle and 1 , 2 , 4 , 5 , 5 round the outside (in this order) then you can make from all numbers from 1 up to 35

there's an interesting consideration about whether to place a small number in the centre (for versatility) or a large number (to get to bigger numbers)

in the solution section of Brian's book it gives 43 as a highest total
this was beaten by a Cambridge trainee teacher in 1996 who got up to 45
then this record was beaten, also in 1996, by an 11 year old who spent a lot of time on it at home - they got from 1 to 46

NRich ran this activity and 46 was the highest number submitted

the easier-to-play-around-with versions are also quite interesting:

  • 2 pieces, the highest is 3
  • 3 pieces, the highest is 7
  • 4 pieces, there are two different solutions that give from 1 to 13
  • 5 pieces, the highest is 19
  • 6 pieces gives 1 to 27
  • 7 pieces, I make 1 to 33
  • 8 pieces, I make 1 to 41
then I gave up...

*A Mathematical Pandora's Box, by Brian Bolt

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