## On the Subject of Dual Sequences

Whilst attempting to make unique random number generators, someone got lazy. Now it’s your problem. Have fun!

The module displays two screens and a toggle button labelled “T”. Each screen displays four three-digit numbers, which will change in every three seconds.

In each three-second interval, a function is applied to each number. There are a total of four unique functions for each screen, but only one of the functions in each screen is shared.

After applying the function to a number, each function moves to the next number to be applied for the next three-second interval, wrapping back to the left if necessary. This applies to all of the functions in both screens.

If the function returns 000, subtract 1 to the number until the function returns a value other than 000. The numbers loop around in the range 000 to 999, e.g. 999 + 1 = 000 and 000 - 1 = 999.

Find the shared function between both screens, then press the toggle button to put the module into submission mode. The top screen will now show four three-digit numbers and a blank bottom screen.

Apply the shared function to each numbers in the top screen, then type it into the bottom screen (using your keyboard, backspace to clear, enter to submit) and press the toggle button again to submit. Note that the toggle button never works unless the bottom screen contains 12 digits.

The module will solve when all the values are correct. Upon an incorrect answer, the module will show the correct digits in green, then revert itself back to its initial state after a strike. The module doesn’t reset.

You may hold the toggle button to regenerate new starting numbers. There will be an audio cue to indicate when to release. Note that the toggle button never works during an animation, as indicated by the absence of the audio cue, in which you could release any time and not trigger anything important.

### The functions

1 N2 + 1. N3 + 1. N+Digital Root of N. 2N. 7N. N/3, rounded down. 999 - N. Absolute difference between N3 and N. Convert to N in binary, then treat the binary digits in N as ternary digits, then convert it back to base 10, plus 1. Sum of all factors of N. Add 1 to every digit (9 becomes 0). Square root of N, rounded up, plus 1. Shift the digits right (123 becomes 312). Reverse the number. Do nothing.