Expert: Scott A Wilson - 2/8/2012

Question
QUESTION: I have been wanting to create a computer program that produces random numbers based on various parameters. Now disregarding that a computer can only produce a quazi random number, and in fact the concept of random might not refer to anything, I need help in some cases. For example if I asked for the initial random number from the computer it will be a number between 0 and 1 which I will multiply out to a whole number and cut off all decimals giving me a number dividable by 10. However if I wanted to then program it to give me a random number from 1 to 26 for example how would I do that? I mean I could tell it to select a random number repeatedly until it selects a number within that range by mistake, but ultimately wouldn't it still be a 1/100 or 1/000 chance (depending on what the random number is multipied out to) of selecting those numbers? It seems like it would be uneven odds even if it has no choice but to select between 1 and 26.

ANSWER: A true place for generating random numbers can be found at http://www.random.org/

To generate a random number from 1 to 26, take the one off the computer times 26,
add 1, and chop off the remaining digits.

To generate a number out of a string of N numbers with the low value being A
and the step being B, so the high number is A+(N-1)B, do the following:

Generate a random number between 0 and 1, then call it X.

Multiply X by N, so now the value is in [0,N)
where [ means 0 is possible, but ) means N is not.

Truncate the value, so now it is an integer in [0,1,2,...,N-2,N-1).

Multiply it by B, so then it is in the set [0,B,2B,3B, ...(N-2)B, (N-1)B).

Add A to it, putting the number in the right range.


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QUESTION: I am familar with that website. But my program needs to be stand alone, and much more flexible than that site. So you're say that if I got a random number between 1 and 100 and wanted a number between 1 and 26 I would multiply what I got by 26 and add 1? Say I got 54. 54x26+1=1405. Now what would I do to reduce that back into the range of between 1 and 26? Divide out 100 and round any decimals? Why add 1? I have no idea what an "N" number is so half your message alludes me. lol.

ANSWER: If the number were desired to be between 1 and 26, don't multiply by 26,
just take mod 26 and add 1.

To reduce that number back in the range of 1 to 26, do a mod 26.

Let's say the number needs to be 1 and 8.

A better set of numbers can be found, but I will use 5 and 1.
The first number will be taken as 1.
Each time, we multiply by 5 and add 1.
1*5+1 = 5+1 = 6, and mod 8 is still 6;
6*5+1 = 30+1 = 31, and mod 8 is 7;
7*5+1 = 35+1 = 36, and mod 8 is 4;
4*5+1 = 21, mod 8 is 5;
5*5+1 = 26, mod 8 is 2;
2*5+1 = 11, mod 8 is 3;
3*5+1 = 16, mod 8 is 0;
0*5+1 = 1, mod 9 is 1;
here, the series would repeat.

So the list of genernated numbers is 1, 6, 7, 4, 5, 2, 3, 0, 1.

These are very small numbers to work with, but this is so the operations are easily understood.
It the numbers were suppose to be between 1 and 8, add 1 to each of the results, but keep the base number the same for next time.  The output would be 2, 7, 8, 5, 6, 3, 4, 1, 2.

One of the major criteria for selecting larger numbers is that they have no factors in common with each other.  For example, if the large number were 100, it is known that 100 = 2*2*5*5.
That means the other two factors (the multiplier and the adder) could not be divisible by 2 or 5.  There needs to be some condition such that each number is random enough from the last number, but that's beyond what I know.


---------- FOLLOW-UP ----------

QUESTION: What is "mod?"

Answer
The term 'mod' is used in mathematics to mean the remainder after division.
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For example, lets look at 25 mod 7.  The largest ineger to multiply 7 by is 3, for 7*3=21,
which is less than 25.  Note that that next higher integer, 4, gives 4*7 = 28,
and that is too high.

Since 7*3 = 21, and we have 25, the answer to 25 mod 7 is 4.
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If we look at n mod 2, the answer will always be 0 or 1.
If n is even, the answer is 0; if n is odd, the answer is 1.
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Suppose we have 47 mod 13.  13*1 = 13, and that is less than 47;
13*2 = 26, and that is less than 47;
13*3 = 39, and that is less than 47; and
13*4 = 52, but that is greater than 47.

Since 4 gives a number too high, 3 is how many times to multiply 13 by.
This 3 is not the answer, but 3*13 = 39, and 47 - 39 = 8,
so the answer is 8,  This says 47 mod 13 = 8.
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N,k,N mod k
1, 5, 1, since 5 doesn't go;
2, 5, 2, since 5 doesn't go;
3, 5, 3, since 5 doesn't go;
4, 5, 4, since 5 doesn't go;
5, 5, 0, since 5 divides evenly;
6, 5, 1, since 6-5=1;
7, 5, 2, since 7-5-2;
8, 5, 3, since 8-5=3;
9, 5, 4, since 9-5=4;
10, 5, 0, since 5 divides evenl;
11, 5, 1, since 11-2*5=11-10=1.

There are three examples with three different ways to explain it.