Number LOGIC
This is not my problem. If it had been mine, I would have included the exponent of three as a letter.
Decode the letters into the proper digits.
The individual numbers of LOGIC are added, that sum is then cubed. The result has the
same as the digits that you began with.
(L+O+G+I+C)^3= LOGIC
Note that only five different digits are used.
Decode the letters into the proper digits.
The individual numbers of LOGIC are added, that sum is then cubed. The result has the
same as the digits that you began with.
(L+O+G+I+C)^3= LOGIC
Note that only five different digits are used.
posted by Ragknot at
12:31 AM
5 Comments:
(0+4+9+1+3)^3=04913... simple
bingo :)
oh! i thought L should not be equal to 0 , as i thought LOGIC was a 5 digit number :P
ok, after the last anon made me realize about 0, i got the following:
L=0;O=0;g=0;i=0;c=0
L=0;O=0;g=0;i=0;c=1
L=0;O=0;g=5;i=1;c=2
L=0;O=4;g=9;i=1;c=3
L=0;O=5;g=8;i=3;c=2
L=1;O=7;g=5;i=7;c=6
L=1;O=9;g=6;i=8;c=3
according to Ragknot's clue about 3 being one of them, the possible ones are:
L=0;O=4;g=9;i=1;c=3
L=0;O=5;g=8;i=3;c=2
L=1;O=9;g=6;i=8;c=3
this is IF L can be 0.
Otherwise, i get a unique solution (which i prefer) so i am goin with that:
L=1;O=9;g=6;i=8;c=3
L+O+G+I+C >= 22 to get a 5 digit number.
L+O+G+I+C =< 35 as 9+8+7+6+5 = 35.
So brute-forcing from 22^3 through to 35^3, reveals LOGIC = 19683 as the only solution, as Vago said.
Even if allow two or more letters to have the same value, only need to try up to 9+9+9+9+9 = 45; and there are still no other solutions.
I see no low labour elegant way of doing it (not that I tried hard) :(
Answer:
(1 + 9 + 6 + 8 + 3)^3 = 19683
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