Computational Techniques
in Theoretical Physics
Homework 2

Suppose that you wish to obtain a decimal digit at random, not using a
computer, which of the following methods would be suitable?

Open a telephone directory to a random place (i.e., stick your finger in
it somewhere) and use the units digit of the first number found on the
selected page.

Same as above, but use the units digit of the page number.

Roll a die that is in the shape of a regular icosahedron, whose twenty
faces have been labeled with the digits 0, 0, 1, 1, ..., 9, 9. Use the
digit that appears on top, when the die comes to rest (A felt table with
a hard surface is recommended for rolling dice).

Expose a geiger counter to a source of radioactivity for one minute (shielding
yourself) and use the units digit of the resulting count. Assume that the
geiger counter displays the number of counts in decimal notation, and that
the count is initially zero.

Glance at your wristwatch; and if the position of the secondhand is between
6n and 6(n+1) second, choose the digit n.

Ask a friend to think of a random digit, and use the digit he names.

Use the formula of linear congruential method to show that, for m=10 and
X_{0}=a=c=7, the generated sequence of random numbers is: 7, 6,
9, 0, 7, 6, 9, 0. What is the sequence for m=30 and X_{0}=a=c=14?

Theorem A. Check each of the random number generators given in the
Table shown in the Lecture against the Theorem A, assert for each case
whether the period is m.