daisy

this problem appeared in one of Brian Bolt's books*
it's promoted a keen interest in getting from 1 up 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 (yes, 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, with a 1 in the centre:

a fairly low
highest number
but you can make all the numbers from 1 up to 25

note that 10 is not 4 + 6 because those regions are not adjacent










another 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 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 - who got from 1 to 46

nrich ran this activity on their website and 46 was the highest number submitted

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

for:

• 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