# This page contains spoilers!

You might have more fun figuring out some of these tricks yourself.

I tried to catalogue only the "open secrets" that tend to come up on Discord.

## 12 Days of Christmas

- The reason Lisp is so short is it has English formatting for numbers built-in (like
`Twelve`

). - You'll have to compress the text to win in many languages.

## brainfuck

- You don't have to skip the first argument if it's
`--`

in your language: that's a perfectly fine brainfuck program producing no output. - If your language has
`eval`

, that's probably the way to go.

## Catalan's Constant

**1/1 − 1/3² + 1/5² − 1/7² + 1/9² …**converges so slowly that it's useless for this problem.- You'll have to look around the internet for a faster approach (or do a lot of math) :)

## Collatz

- You can try a "zero-based" instead of "one-based" procedure instead: modify the formula so that instead of
**10 → 5 → 16 → 8 → 4 → 2 → 1**you compute**9 → 4 → 15 → 7 → 3 → 1 → 0**(everything offset down by one). The stopping times are the same, but the loop bounds and halt check might be shorter.

## Emirp Numbers

- There are only 36 numbers to print, so hardcoding them might work.

## CSS Colors

`args`

is always a complete permutation of all possible inputs.- So you can use
`arg => sorted(args).index(arg)`

as a perfect hash function. - Unfortunately this trick doesn't apply to other holes (anymore)

## Evil Numbers, Odious Numbers

- Always exactly one of
`{2n, 2n+1}`

is evil (and the other is odious), so you can hardcode 25 bits. - OK, here are some bigger spoilers.

## Fibonacci

- There is something shorter than
`t=a;a=b;b+=t;`

(you can avoid a temp variable in any language).

## Happy Numbers

- There are only 32 numbers to print, and they all fit in a byte, so you can try a "hardcode" approach.

## ISBN

**− 10a − 9b − 8c − … − 2i (mod 11)**is just**a + 2b + 3c + … + 9i (mod 11)**.

## Lucky Tickets

## Niven Numbers

- There is a shorter formula for two-digit numbers, that also happens to work for 100.

## Pernicious Numbers

- Forget primality: you only have to worry about popcount = 2, 3, or 5.
- In other words, popcount ≠ 1 (mod 3).
- There is a
*really*short magic formula, using a bitwise operator.

## Prime Numbers

- https://en.wikipedia.org/wiki/Primality_test
- A fun bit of history: https://en.wikipedia.org/wiki/Chinese_hypothesis

## Proximity Grid

- Snake-like path length in a maze https://oeis.org/A331968/

## Quine

- In some compiled langs you can (sadly) read the source file from
`/tmp/code.abc`

.

## United States

- Try to create some kind of a hash table or an advanced regex.

## Vampire Numbers

- Checking all the numbers will likely time out. Try to find a shortcut, or approach the problem from the opposite direction.

## λ, π, τ…

- If your language has bignums, then usually you want to compute
`floor(10^1000 * π)`

and then print that but with a decimal point squeezed in. - See primo's answer to a question about how to calculate Conway's constant.