## On the Subject of the Gamepad

Oh, the layout of the buttons on this thing takes me back to my childhood! Except I didn't expect to see that on a time bomb, even. Play time is over, I suppose.

• Two 2-digit numbers will appear on the top LCD display. The bottom has eight keys: the input keys (◀▲▼▶AB), Return, and Backspace.
• Determine the correct command, made of two subcommands, to input, depending on the properties of the two numbers. Use the first match.
• The two numbers are notated x and y. Individual digits are notated as abcd. A number followed by n means a multiple of that number.
Global Overrides If x = 11n, switch the first keypress with the second, and the fifth with the seventh. If a = 1 + d, switch the third and fourth keypresses, as well as the sixth and eighth. If x or y is a highly composite number, switch the order of the subcommands. If x and y are perfect squares, flip the entire sequence. Apply all matches after determining the two commands.
First Subcommand
x is prime ▲▲▼▼
x = 12n A◀◀
a+b = 10 AND the last digit of serial number is odd AB◀▶
x = 6n + 3 OR x = 10n + 5 ▼◀A
x = 7n AND y ≠ 7n ◀◀▲B
x = c × d A▲◀◀
x is a perfect square ▶▶A
x = 3n – 1 OR bomb has unlit ind. labeled SND AB
60 ≤ x < 90 AND bomb has no batteries BB▶◀
x = 6n ABA
x = 4n ▼▼◀▲
else AB
Second Subcommand
y is prime ◀▶◀▶
y = 8n ▼▶B
c - d = 4 AND bomb has a Stereo RCA A▼▼
y = 4n + 2 OR bomb has lit ind. labeled FRQ B▲▶A
y = 7n AND x ≠ 7n ◀◀▼A
y is a perfect square ▲▼B
y = a × b A▲◀▼
y = 4n – 1 OR bomb has a PS/2 port BBB
c > d AND bomb has 2 or more batteries AA▲▼
y = 5n BAB
y = 3n ▶▲▲◀
else BA

## Appendix MathConcepts: Mathematical Concepts

This appendix contains a brief overview of some mathematical concepts used in the Gamepad module.

### Prime Numbers

A prime number is a counting number (positive whole number) that can only be divided by 1 and itself. In other words, there is no way to share a prime number of donuts equally among any number of friends (unless you have as many friends as donuts!).

Prime numbers below 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

### Perfect Squares

A perfect square is any whole number multiplied by itself.

Perfect squares below 100 are: 1, 4, 9, 16, 25, 36, 49, 64, 81.

### Highly Composite Numbers

A highly composite number (HCN) has more divisors than any smaller positive integer. For example, 6 can be divided by 1, 2, 3, and 6, which is more than the last HCN, 4, which has 1, 2, and 4. 8 can be divided by 1, 2, 4, and 8, but a smaller number (6) has an equal number of divisors, so it is not a HCN.

Highly composite numbers below 100 are: 1, 2, 4, 6, 12, 24, 36, 48, 60.