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mahmit2012
Number 3 and its magic powers. Does anybody know how the set of 1 3 9 27 81,... with two operations + and - can generate all integers, each member is used once. For example:32=27+9-3-1
1=1 2=3-1 3=3 4=3+1 5=9-3-1 6=9-3 7=9-3+1 8=9-1 9=9 10=9+1 11=9+3-1 12=9+3 13=9+3+1 so we can make 1-13 with 1,3,9 14=27-13 15=27-12 16=27-11 .... 28=27+1 29=27+2 ... 40=27+13 It shows we could make all 1-40 now 41=81-40 42=81-39 ..... 100=81+19 ... 121=81+40 then we can continue and proof by induction method.