A big number N becomes 6*N if you take its last digit and place it as its first like transforming 123466 into 612346.
REM: Big big number!
Find it.
1/59 = 0.0169491525423728813559322033898305084745762711864406779661016949 (period 58)
2/59 = 0.0338983050847457627118644067796610169491525423728813559322033898 (period 58)
....
6/59 = 0.1016949152542372881355932203389830508474576271186440677966101694 (period 58)
Note that the digits here are identical to 1/59 except for the first and last one.
Moving the decimal point to the end gives the solution for b.
There are 10 numbers between 0 and 100 that end in 9 (needed for the puzzle to 'work'). To have a chance of a long period we need the number to be prime, which eliminates 9,39,49,69,99.
The remaining prime candidates are 19 (period 18), 29 (period 28), 59 (period 58), 79 (period 13), 89 (period 44). So of the available candidates, 59 is by far the most challenging.
Good puzzle!
Edited on March 25, 2022, 12:24 am
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Posted by broll
on 2022-03-25 00:22:32 |
Why are the numbers so big?
