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 second-hand 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 X₀=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 X₀=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.