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 Possible Percent Problems Part 2 (Posted on 2010-01-11)
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?

 No Solution Yet Submitted by Jer No Rating

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 re: solution | Comment 2 of 3 |
(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  4445  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  6465  66  68  69  70  71  72  73  74  75  76  77  78  79  80  81  82  83  84  8586  87  88  89  90  91  92  93  94  95  96  97  98  99  100`
` `
`DEFDBL A-ZDIM 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 bPRINT`

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

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