If you moved the 3 at the end of a certain large number to the beginning, it would be the same as multiplying it by 3. What is the number?

(In reply to re: Standard solution by Richard)

This didn't use the "standard" solution, but here's a rundown for various move-by and multiply-by values, with the length of the number shown below the number:

Move the 2 , mult. by 2 .
105263157894736842
 18
Move the 3 , mult. by 2 .
157894736842105263
 18
Move the 3 , mult. by 3 .
1034482758620689655172413793
 28
Move the 4 , mult. by 2 .
210526315789473684
 18
Move the 4 , mult. by 3 .
1379310344827586206896551724
 28
Move the 4 , mult. by 4 .
102564
 6
Move the 5 , mult. by 2 .
263157894736842105
 18
Move the 5 , mult. by 3 .
1724137931034482758620689655
 28
Move the 5 , mult. by 4 .
128205
 6
Move the 5 , mult. by 5 .
102040816326530612244897959183673469387755
 42
Move the 6 , mult. by 2 .
315789473684210526
 18
Move the 6 , mult. by 3 .
2068965517241379310344827586
 28
Move the 6 , mult. by 4 .
153846
 6
Move the 6 , mult. by 5 .
122448979591836734693877551020408163265306
 42
Move the 6 , mult. by 6 .
1016949152542372881355932203389830508474576271186440677966
 58
Move the 7 , mult. by 2 .
368421052631578947
 18
Move the 7 , mult. by 3 .
2413793103448275862068965517
 28
Move the 7 , mult. by 4 .
179487
 6
Move the 7 , mult. by 5 .
142857
 6
Move the 7 , mult. by 6 .
1186440677966101694915254237288135593220338983050847457627
 58
Move the 7 , mult. by 7 .
1014492753623188405797
 22
Move the 8 , mult. by 2 .
421052631578947368
 18
Move the 8 , mult. by 3 .
2758620689655172413793103448
 28
Move the 8 , mult. by 4 .
205128
 6
Move the 8 , mult. by 5 .
163265306122448979591836734693877551020408
 42
Move the 8 , mult. by 6 .
1355932203389830508474576271186440677966101694915254237288
 58
Move the 8 , mult. by 7 .
1159420289855072463768
 22
Move the 8 , mult. by 8 .
1012658227848
 13
Move the 9 , mult. by 2 .
473684210526315789
 18
Move the 9 , mult. by 3 .
3103448275862068965517241379
 28
Move the 9 , mult. by 4 .
230769
 6
Move the 9 , mult. by 5 .
183673469387755102040816326530612244897959
 42
Move the 9 , mult. by 6 .
1525423728813559322033898305084745762711864406779661016949
 58
Move the 9 , mult. by 7 .
1304347826086956521739
 22
Move the 9 , mult. by 8 .
1139240506329
 13
Move the 9 , mult. by 9 .
10112359550561797752808988764044943820224719
 44

Produced by

OPEN "movxmulx.txt" FOR OUTPUT AS #2
FOR movthe = 2 TO 9
 FOR multby = 2 TO movthe
  ct = 0
  PRINT #2, "Move the"; movthe; ", mult. by"; multby; "."
  divisor = multby
  temp = movthe
  quot$ = ""
  DO
    q = temp \ divisor
    r = temp MOD divisor
    quot$ = quot$ + LTRIM$(STR$(q))
    ct = ct + 1
    IF q = movthe AND r = 0 THEN EXIT DO
    temp = r * 10 + q
  LOOP

  PRINT #2, quot$
  PRINT #2, ct
 NEXT
NEXT

CLOSE

Posted by Charlie on 2004-03-02 08:34:50