median
don steward
mathematics teaching 10 ~ 16

Tuesday, 7 December 2010

Zorro using 1 to 7

zorro
use digits1 to 7 (once only) so that the lines of three have the same total

what totals are possible and how many variants are there? prove that the middle must be even

prove that 7 and 6 must not be in the same line

ignoring unimportant swaps, show that there are: 
two solutions with 2 in the middle
three with 4 in the middle 
two with 6 in the middle

prove that only totals of 11, 12 and 13 are possible
why is a total of 14 impossible?


















this is the same as a task called 'Haitch'
Graeme Brown produced an Excel interactive version for NRich here



                                                                                                                               

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