Theorem is a free daily tile puzzle about scoring high. You swap tiles on a grid to match today's three rules, and your score is base times multiplier. You get three tries per grid to reach bronze, silver or gold.
How do you play Theorem?
- Pick a size: Easy (3×3), Medium (4×4) or Hard (5×5). Press Play.
- Read "Today's multipliers" above the grid. These are the day's three rules.
- Drag a tile onto another tile to swap them. Every tile has a shape, a color and a number from 1 to 5.
- Watch the count beside each rule. It shows how many times that rule matches on the board right now. Tap a rule to light up its matches.
- When you like the layout, press Submit. The game counts up your base, your multiplier and your score.
- You get three submits per grid. Your best one counts.
Your layout is saved as you go, so you can leave and come back the same day.
How is the score worked out?
Your score is base × multiplier. Here's where each part comes from.
Base starts as the sum of every tile's number. Swapping never changes that sum, since the same tiles stay on the board. Some rules add more to the base, shown by a purple chip such as "+sum" or "+5".
Multiplier starts at 1. Every match of every rule adds 1 to it, purple rules included.
So a purple rule helps twice: once on the base and once on the multiplier. An orange rule only adds to the multiplier.
A worked example
Say it's an Easy grid and the tile numbers add up to 27. Today's rules are:
- Same color side by side
- Three rising, left to right
- Neighbors summing to 5 (purple, +5 per match)
You arrange the tiles so there are 4 same-color pairs, 1 rising row and 2 pairs that sum to 5. Then:
Multiplier: 1 + 4 + 1 + 2 = 8 Base: 27 + (2 × 5) = 37 Score: 37 × 8 = 296
Now find one more same-color pair without breaking anything. The multiplier goes to 9 and the score to 333. Every match counts.
How do medals work?
The bar above the score fills from nothing to bronze, silver and gold. The medal lines are set fresh for each grid each day, based on the best board the game's own search could find.
Gold finishes the grid, though you can keep submitting if you have tries left and want a higher score. When a grid is finished, the results screen sets your score beside the best board's score. Show best board reveals the layout the search found. If you beat it, the results say "New high!"
How do you get Extreme?
Extreme is a 6×6 grid. It only appears after you get gold on Easy, Medium and Hard that same day.
Extreme has a twist: a few tiles, between 2 and 5, are locked in place and marked with a small cross. You can't move them, and you can't swap another tile onto their square. You build the rest of the layout around them.
Tips for a higher score
- Sort for one rule first. Pick a rule and arrange the grid to satisfy it. Then work out how to change that arrangement to pick up the next rule, without breaking the first. It's much easier than juggling all three at once.
- Count before you submit. Add the numbers beside the rules and add 1. That's the multiplier you're about to get.
- Look for overlap. A tile can count for more than one rule at once. If today has both a color rule and a number rule, a green 3 next to a green 4 can count for each.
- Favor purple rules when you can. They raise the base and the multiplier together.
- Check for "N/A". Some rules can't happen with a given grid's tiles. They're marked N/A, so don't spend swaps on them.
- Don't rush the first try. You only get three, and swapping costs nothing until you press Submit.
How is Theorem scored?
Each grid has its own score and medal. Signed-in players get a daily leaderboard for each grid size, plus a friends-only board. Higher scores rank first, and fewer tries breaks a tie.
Your results also track a medal streak and a gold streak for each size, your high score for each size, and your gold, silver and bronze counts.
How do you share your result?
The Share button gives you two choices. Spoiler free copies the puzzle number, the difficulty, your medal if you earned one and your best score:
Theorem #208 / Hard / 🥇 412 perdiem.games/theorem
With spoilers adds a picture of your finished board. Pick spoiler free if your friends haven't played yet.
Common questions
Are the rules the same on every grid?
Yes. The day's three rules apply to all four sizes. A new set arrives the next day.
Is there a timer?
No. Take as long as you like. Only your score and your number of tries count.
Can I play past days?
Yes. Past days open from the week strip on your results screen. Only today's puzzle counts for the leaderboard.
Do I need an account?
No. Theorem is free and runs in your browser. An account keeps your streaks and medals across devices and adds leaderboards and friends.