Question

The challenge:

The shortest code by character count that will generate a series of (pseudo)random numbers using the Middle-Square Method.

The Middle-Square Method of (pseudo)random number generation was first suggested by John Von Neumann in 1946 and is defined as follows:

R_n+1 = mid((R_n)², m)

For example:

3456² = 11943936

mid(11943936) = 9439

9439² = 89094721

mid(89094721) = 0947

947² = 896809

mid(896809) = 9680

9680² = 93702400

mid(93702400) = 7024

Another example:

843² = 710649

mid(710649) = 106

106² = 11236

mid(11236) = 123

123² = 15129

mid(15129) = 512

512² = 262144

mid(262144) = 621

621² = 385641

mid(385641) = 856

856² = 732736

mid(732736) = 327

327² = 106929

mid(106929) = 069

69² = 4761

mid(4761) = 476

476² = 226576

mid(226576) = 265

Definition of mid:

Apparently there is some confusion regarding the exact definition of mid. For the purposes of this challenge, assume that you are extracting the same number of digits as the starting seed. Meaning, if the starting seed had 4 digits, you would extract 4 digits from the middle. If the starting seed had 3 digits, you would extract 3 digits from the middle.

Regarding the extraction of numbers when you can’t find the exact middle, consider the number 710649. If you want to extract the middle 3, there is some ambiguity (106 or 064). In that case, extract the 3 that is closest to the beginning of the string. So in this case, you would extract 106.

An easy way to think of it is to pad zeroes to the number if it’s not the right number of digits. For example, if you pad leading-zeroes to 710649 you get 0710649 and the middle 3 digits now become 106.

Test cases:

Make no assumptions regarding the length of the seed. For example, you cannot assume that the seed will always be 4-digit number

A starting seed of 3456 that generates 4-digit random-numbers should generate the following series (first 10):

9439, 947, 9680, 7024, 3365, 3232, 4458, 8737, 3351, 2292

A starting seed of 8653 that generates 4-digit random numbers should generate the following series (first 10):

8744, 4575, 9306, 6016, 1922, 6940, 1636, 6764, 7516, 4902

A starting seed of 843 that generates 3-digit random numbers should generate the following series (first 10):

106, 123, 512, 621, 856, 327, 69, 476, 265, 22

A starting seed of 45678 that generates 5-digit ranom numbers should generate the following series (first 10):

86479, 78617, 80632, 1519, 30736, 47016, 10504, 3340, 11556, 35411

As far as leading zeroes are concerned, the answer is no leading zeroes should be displayed :).

Answer 1

dc 26/37 chars

26 chars the function for a single number:

?dZsl2^dZ1+ll-2/Ar^/All^%p

37 chars with a 10 cycles loop:

?dZsl[2^dZ1+ll-2/Ar^/All^%pdzB>L]dsLx

Explanation of the function:

?            Input n
dZ           calculate number of digits
sl           store in register l
2^           calculate n^2
dZ           calculate number of digits of square
1+ll-2/Ar^/  n/(10^((squaredigits+1-l)/2)) int division truncates last digits 
All^%        n%(10^l) modulus truncates first digits
p            print the number

Test:

dc msml.dc
45678
86479
78617
80632
1519
30736
47016
10504
3340
11556
35411