Season 2 • Episode: Better or Worse

NUMB3RS - Season 2 - "Better or Worse" - Creating Random Numbers

Topic: Pseudo-random NumbersTI Classroom PDF

Step 1 of 5

1Don't Rule for Randomness

Background Scenario:

In the NUMB3RS episode 'Bettor or Worse', Agent Don Eppes needs to assign random two-digit passcodes to 40 members of his FBI task force. Recalling a conversation with his brother Charlie, Don attempts to quickly create a rule to generate pseudo-random numbers starting from an initial 'seed'. We will investigate how Don's deterministic rule works, why it is called 'pseudo-random', and the limitations of recursive number generators.

Don proposes the following rule to generate two-digit codes:

Multiply the seed by $41$ .
Add $35$ .
Divide by $101$ .
Take the first two decimal places of the result as your new pseudo-random number.

Let's walk through an example. Suppose our starting seed ( $x_0$ ) is $29$ : $\frac{29 \cdot 41 + 35}{101} = \frac{1189 + 35}{101} = \frac{1224}{101} \approx 12.1188...$ Taking the first two decimal places, our next number ( $x_1$ ) is $11$ .

Interactive LCG Sandbox (Don't Rule)

Initial Seed ($x_0$):29

Simulation Speed:0.50

2D Spectral Plane Pattern PlotPairs of Consecutive Numbers: $(x_n, x_{n+1})$

True randomness covers space uniformly. Poor pseudo-random formulas group points along distinct linear paths, exposing clear patterns.

x_n (Min: 0.00, Max: 1.00)

x_n+1 (Min: 0.00, Max: 1.00)

Iteration	Seed ($x_n$)	Formula: $(41x_n + 35)/101$	Output ( $x_{n+1}$ )

1Don't Rule for Randomness

Interactive LCG Sandbox (Don't Rule)

2D Spectral Plane Pattern PlotPairs of Consecutive Numbers: (xn,xn+1)(x_n, x_{n+1})(xn​,xn+1​)

2D Spectral Plane Pattern PlotPairs of Consecutive Numbers: $(x_n, x_{n+1})$