median
don steward
mathematics teaching 10 ~ 16

Sunday, 13 February 2011

two 2-digit subtraction

using all four of the digits
5 , 2 , 8 , 7
how many possible positive answers can be obtained?







establish that there are 12 possible positive results:  (7 , 13 , 14 , 25 , 26 , 29 , 31 , 35 , 47 , 53 , 58 and 62)

  • if you used any four consecutive numbers are there any patterns in the results? (not too many...)
  • prove that 31 is the largest possible result and 7 is the smallest for any four consecutive numbers
  • try to get a result of 9 (or a multiple of 9) with four consecutive numbers (e.g. 85 - 76) and then look at it backwards (67 - 58) - why is there still a result of 9?

which four digits were used to obtain all of the different answers:
7 , 9 , 11 , 13 , 18 , 22 , 29 , 29 and 31?

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