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Mixing Meters, Yards and Months (Posted on 2007-10-04) Difficulty: 3 of 5
If we assume that 11 meters = 12 yards, what is the smallest integral number of meters that can be converted to its equivalent integral number of yards simply by rearranging the order of the digits of the number?

What if we do the same with the actual exact equivalents?: 1143 meters = 1250 yards.

Then try your hand at 228 solar months = 235 lunar months (the 19-year Metonic cycle).

  Submitted by Charlie    
Rating: 3.0000 (3 votes)
Solution: (Hide)
With 11 meters = 12 yards, 1683 meters = 1836 yards.
With 1143 meters = 1250 yards, 2582037 meters = 2823750 yards.
With 228 solar months = 235 lunar months, 3389904 solar months = 3493980 lunar months.

DEFDBL A-Z
CLS
DO
 y = y + 228
 m = m + 235
 yd$ = LTRIM$(STR$(y))
 mt$ = LTRIM$(STR$(m))
 IF LEN(yd$) = LEN(mt$) THEN
   good = 1
   FOR i = 1 TO LEN(yd$)
    ix = INSTR(mt$, MID$(yd$, i, 1))
    IF ix = 0 THEN good = 0: EXIT FOR
    mt$ = LEFT$(mt$, ix - 1) + MID$(mt$, ix + 1)
   NEXT
   IF good THEN
    PRINT y, m
    ct = ct + 1
    IF ct > 45 THEN END
   END IF
 END IF
LOOP

The first portion of the problem is Enigma No. 1459, by Richard England, New Scientist, 8 September 2007.

Others:

Part 1:

   1683     1836
   5247     5724
  16830    18360
  26829    29268
  31284    34128
  52371    57132
  52470    57240
  53658    58536
  62568    68256
  80487    87804
 125136   136512
 166518   181656
 168300   183600
 169488   184896
 252747   275724
 268290   292680
 312741   341172
 312840   341280
 423621   462132
 523710   571320
 524700   572400
 536580   585360
 591426   645192
 604395   659340
 625680   682560
 680724   742608
 732996   799632
 804870   878040
 881694   961848
 896742   978264
 899613   981396
1016829  1109268
1028115  1121580
1251360  1365120
1302246  1420632
1318284  1438128
1349271  1471932
1438569  1569348
1456983  1589436
1465992  1599264
1516284  1654128
1526976  1665792
1616373  1763316
1637658  1786536
1665180  1816560
1675278  1827576

Part 2:

   2582037       2823750
  15903702      17392500
  20296251      22196250
  25820370      28237500
  30542103      33401250
  89733501      98133750
 105575481     115458750
 108682155     118856250
 109001052     119205000
 159037020     173925000
 168429051     184196250
 192480057     210498750
 202962510     221962500
 250498737     273948750
 258203700     282375000
 305421030     334012500
 307159533     335913750
 332650719     363791250
 347052519     379541250
 360425619     394166250
 401285583     438851250
 402067395     439706250
 405832437     443823750
 405914733     443913750
 420059358     459382500
 425316015     465131250
 432681507     473186250
 435376701     476133750
 451877049     494178750
 506233557     553623750
 512055999     559991250
 513475605     561543750
 530510877     580173750
 543009582     593842500
 602581599     658991250
 605688273     662388750
 605966022     662692500
 612045639     669341250
 621509679     679691250
 651012795     711956250
 673520751     736571250
 684301527     748361250
 705081267     771086250
 707015223     773201250
 708475977     774798750
 728659071     796871250

Part 3:

 3389904       3493980
 4795524       4942755
13549356      13965345
14047992      14479290
16155396      16651395
19278540      19870425
19574028      20174985
20025468      20640285
20651328      21285360
21523428      22184235
23542596      24265395
25063128      25832610
26780652      27602865
31274532      32234715
31352508      32315085
33145956      34163595
33308064      34330680
33404508      34430085
33855948      34895385
33899040      34939800
34315596      35369145
35054316      36130545
35456508      36545085
35866908      36968085
36117252      37226115
43705548      45047385
45478476      46874745
47955240      49427550
50126256      51665220
50503824      52054380
54796608      56478960
55976508      57695085
56735748      58477635
64135260      66104325
64757016      66745170
66103128      68132610
66384252      68422365
70617528      72785610
72234504      74452230
74360376      76643370
82096416      84616920
83050596      85600395
85402188      88024185
91985004      94809105
93454236      96323445
94580784      97484580

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Answer to part (iii)K Sengupta2023-12-15 20:17:58
Answer to parts (i) and (ii)K Sengupta2008-11-19 00:19:58
re: Solution (corrected)brianjn2007-10-15 04:08:30
SolutionSolution (corrected)badger2007-10-11 11:35:13
SolutionComputer solutionsbadger2007-10-11 11:25:40
re(2): Improvement on brute force?brianjn2007-10-05 10:26:41
re: Improvement on brute force?Leming2007-10-04 16:26:33
Improvement on brute force?Jer2007-10-04 15:26:36
Some ThoughtsSolution ala brute forceLeming2007-10-04 11:09:24
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