some aspects of this problem can lead to proof: that the central little triangle must be 19 when the big triangle totals are 46; that there are only two (essentially) different solutions, because 17 has to go with either (9 and 1) or (7 and 3)

other totals are possible:

there are two different solutions with big triangle totals of 34, 38 and 42

the middle numbers for these are 1, 7 and 13 respectively

you can prove that 3 must be a factor of (the middle number minus 1)

a lot of thinking can determine which numbers have to go with which other numbers

it's also good practice at addition, which could be done using cards with dot arrangements for those who might find this helpful

## No comments:

Post a Comment