median
don steward
mathematics teaching 10 ~ 16

Sunday, 9 December 2007

two reversal problems

(1) there is only one 2-digit number which:

when 2 is subtracted from it and this result is doubled
it becomes the reverse of the original 2-digit number

for example, starting with 36: 36 - 2 is 34
and
this doubled is 68 which is not the reverse of 36 (but isn't a million miles off)
prove that there can only be one solution


(2) find six consecutive numbers 
so that the sum of the last three numbers is the reverse of the total of the first three numbers

there are two such sets of six
the smallest set involves digits (all less than 10)

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