median
don steward
mathematics teaching 10 ~ 16

Monday, 3 March 2014

fiveways

use the digits 1 to 9, once only so that
all five lines (of three squares) have the same total

can you find the one way to make lines total 13?
there is also only one way to make lines total 17

there are four ways (ignoring rotations etc.)
to make the lines sum to 12 and 18

totals of 14 and 16 can also be made in 4 different ways (each)



you can fairly easily prove that totals of 11 or lower and 19 or higher are impossible

15 has four solutions as well (I think...) although it appears that there should be more...


although a sytematic approach can be helpful, it is fairly easy to find solutions by playing around
the task provides practice in adding digits repeatedly
and results can be collected as a class

what is probably not obvious to many students is the complementartity: once you have one solution you have another solution by using individual complements to 10 (which is why the sets of results for a particular total are symmetrical)

4 key positions can determine the rest of the grid - it might be convenient to have these as the four corners

the digits in the top right and bottom left hand corner positions are key: they need three ways to combine with different pairs of digits to make the target total

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