Given whole numbers a and b we can find the ratio a/b and round it to the nearest whole percent.

A value of b is said to generate any percentage that is a possible value of a/b.

For example b=15 generates seven percentages between 0 and 50 including 27% = 4/15 and 47% = 7/15.
There is no smaller b that generates 47% but there is a smaller b (11) that generates 27% (3/11)

What is the smallest value of b such that for every percentage between 0 and 50 that it generates there is a smaller b that also generates it?

(In reply to solution by Dej Mar)

Verified that 20 is the smallest:

The complete list of b's that satisfy the criterion:

20  22  24  25  26  27  28  30  31  32  33  34  36  37  38  39  40  42  43  44
45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64
65  66  68  69  70  71  72  73  74  75  76  77  78  79  80  81  82  83  84  85
86  87  88  89  90  91  92  93  94  95  96  97  98  99  100

DEFDBL A-Z
DIM did(50)
FOR b = 1 TO 100
 good = 1
 FOR a = 0 TO b / 2
  pct = INT(100 * a / b + .5)
  IF did(pct) = 0 THEN good = 0
  did(pct) = 1
 NEXT a
 IF good THEN PRINT b;
NEXT b
PRINT

Posted by Charlie on 2010-01-11 14:34:53