#math game

[mathhombre]

COMBO

Made a little arithmetic game in GeoGebra for my summer algebra students. (Basically Proof! except it always works.) Loving that there are always more than what I put in there. Play in GeoGebra.

[tropylium]

Here’s a math game I recently invented, vaguely inspired by metroidvania mechanics. (Not sure if I want to call it “Mathroidvania” or think of something better.)

The game begins at some particular positive integer with an empty inventory. Your task is to descend down to 1 in a finite series of moves.

There are two types of moves. For one, you can either Sᴛᴇᴘ to an adjacent integer (from n up to n+1 or down n-1). For two, you can Jᴜᴍᴘ, either up to a multiple of the current integer (from n to nm); or, from a composite integer, down to a factor of it (from n to n/m).

Movement is limited by several further rules. Jumping has two general rules: (1) it is possible only if the required factor / divisor m is in your Iɴᴠᴇɴᴛᴏʀʏ; (2) jumping all the way down from n to 1 is not a valid move.

Movement, as well as building up your inventory, is further subject to different rules between three groups of numbers: Pʀɪᴍᴇs, Pʀɪᴍᴇ ᴘᴏᴡᴇʀs and “Cᴏᴍᴘᴏsɪᴛᴇs” (the last group, in the game’s context, excluding prime powers).

– Primes are the primary roadblocks in the game. You cannot step in either direction from a prime that is not in your inventory. (There are no moves from a prime starting position; I’ve considered adding a rule allowing an “inventoryless jump” up to p², though.)

– Prime powers are secondary roadblocks. You can neither step down nor jump down from a prime power. However, visiting a prime power will add the corresponding prime to your inventory. Prime powers itself cannot be added to your inventory; you can simply (will have to) jump twice if you have the corresponding prime in your inventory.

– “Composites” are the basic terrain: you can always step up or step down from a composite, and visiting a composite will add that composite to your inventory.

I give under the cut a 20-move solution to the game starting from 4. Games starting from 6, 9, 10, 14, 15, 16 are also relatively simple (they quickly reduce to the same ending as this). The game starting from 12, if solvable, is the first substantially complex case…

Game positions are given in the notation N {P}, with N being your location and {P} your “reduced” inventory (only consisting of those integers used during the solution). Inventory numbers used for jumps are bolded.

start at 4 {2} (4 = 2²) jump up to 8 {2} step up to 9 {2 3} (9 = 3²) step up to 10 {2 3} jump up to 20 {2 3} step up to 21 {2 3} jump down to 7 {2 3} jump up to 14 {2 3} step up to 15 {2 3} step up to 16 {2 3} jump up to 48 {2 3} jump down to 24 {2 3} step up to 25 {2 3 5} (25 = 5²) step up to 26 {2 3 5} step up to 27 {2 3 5} step up to 28 {2 3 5} jump down to 14 {2 3 5} step up to 15 {2 3 5} jump down to 3 {2 3 5} step down to 2 {2 3 5} step down to 1 {2 3 5}

[mymathematics]

The Dollar Game

Great video

[mathhombre]

Multiplication Mix Up

Inspired by Denise Gaskin's math game post, https://denisegaskins.com/2026/05/18/math-game-monday-scrambled-times-tables/, I wanted to implement the puzzle in GeoGebra. The multiplication chart has been messed up! The side and top numbers are scrambled. Can you deduce them? The clue bar gets you more, less or different clues. New gets you a new puzzle. There may be more than one solution that fits a batch of clues, but there is always at least one solution!

Play in GeoGebra.

[mathhombre]

The L Game

Quite a few math games and activities at their website, African Institute for Mathematical Sciences School Enrichment Center. Seen at their FB page.

[mathhombre]

MAD Deviation

Mathober Day 2: Deviation.

I made a GeoGebra guessing game for the most underappreciated statistic, mean absolute deviation.

Here's two examples:

So what would you guess these have?

Answers in a comment!

[mathhombre]

Quaternion Games

Was reading Jim Propp's excellent expository piece on quaternions and it had links to three math games I wanted to remember.

Block'n'Roll (connection is with rotations)

Groupdoku

Hamilternion card game - practice with multiplication, I'd like to develop this one.