median
don steward
mathematics teaching 10 ~ 16

Friday, 13 March 2009

nineteen

using any four consecutive digits along with any operations and brackets, can you make 19?

starting with 1: 
(2 + 4) x 3 + 1
4 x 5 – 3 + 2
2 + 3 x 4 + 5

and other ways using four consecutive digits:
 

starting with 3: 3 x 6 + 5 – 4
starting with 4: 5 x 6 – 4 – 7   or  4 x 5 + 6 – 7
starting with 5: (8 – 6) x 7 + 5
starting with 6: 9 x 8 ÷ 6 + 7  or  8 ÷ 6 x 9 + 7 (a tough one... to find)

it’s interesting that from those starting with 1:
4  x  5 – 3 = 3  x  4 + 5
and that from those starting with 4:
5  x  6 – 4 = 4  x  5 + 6

explore a generalisation for these results
and try to prove it
for any three consecutive numbers . . .

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