0–100 Year Challenge

The 0–100 year challenge is simple: use the digits of the year, each exactly once, to make all the numbers from $0$ to $100$ inclusive.

The introductory challenge allows the digits to appear in any order. For instance, to make $20$ from $2023$ :

(3 - 2) imes 20 = 20

But we don’t do that here. We do the elite challenge, where all 4 digits must appear exactly in their original order. For instance, to make 100 from 2024:

20^2 / 4 = 100

Naturally, the difficulty of the challenge depends entirely on what operations you allow. Agreeing on this is mathematically impossible, so we’ll define several rulesets in increasing levels of breadth.

ruleset	allowed operations	description
Core	$() \\ + \\ - \\ \cdot \\ / \\ x^y \\ ! \\ xy$	Only the simplest of arithmetic operations, as well as combining digits to form multi-digit numbers. So far, no years are 100%-able at this level.
Further Core	$.x$	Allows conversion to decimal without a leading $0$ . Technically valid, right?
Expansion	$\log_x(y) \\ \arcsin(x) \\ \arccos(x) \\ \arctan(x)$	These make the challenge SO much more fun.
Further Expansion	$x!!$
Absurd Expansion	$\text{round}() \\ \text{floor}() \\ \text{ceil}() \\ \sqrt{}$	At this point, the challenge isn’t fun anymore.

The goal of these rulesets is to open up the possibilities such that it’s still possible to 100% the challenge, whilst not removing the elements of fun and challenge.¹

So, which ruleset do I solve for? All of them, of course! Why settle with just one answer when you can find a multitude of unique ways to do it.

Expansion is definitely my favourite ruleset, but for each number, I try to find the strictest solution that I can – i.e. that which follows the strictest ruleset – and the most creative solutions.

It feels like Mojang adding redstone features to Minecraft, lmao.↩

2024

2025