Tips & strategy

Mathdle rewards two very different skills: finding the obvious expressions quickly, and constructing the deep ones that nobody else spots. This page is everything that helps with the second part.

Start with the cheapest hits

Before you go hunting for clever constructions, sweep up the small stuff. The two expressions worth the fewest points are also the easiest to miss when you skip past them looking for pangrams.

• Center plus one other tile. Run through every tile combined with the center using +, −, ×, and ÷. If the target is 12 and your tiles include a 3 and a 4 with 9 as the center, both 3 + 9 and 4 × 3 are points on the board.
• Center plus two tiles. Same loop, one tile deeper. A surprising fraction of catalogued expressions live here, especially on Easy and Medium.
• Doubles and halves of the target. If two tiles sum to the target, the center can usually plug in via a difference or a multiplier. If two tiles multiply to the target, look for a center tile that adds and subtracts to zero somewhere.

Work backwards from the target

Forward search (“what can I build?”) is exhausting because the branching factor explodes. Backwards search (“what equals the target?”) is bounded by the target itself. Factor it. If the target is 72, you immediately know that any pair of tiles whose product is 72 — or whose product divides into it cleanly — is a candidate skeleton.

Factoring also tells you when to bring in division. Mathdle accepts division only when the result is exact: ÷ is real-rational, not integer division. If the target is 7 and you have an 8 and a 56, then 56 ÷ 8 = 7 is a clean construction. If you have a 6 instead, 56 ÷ 6isn't rational over the tile values you need, and the engine will reject it.

Distribution is where the volume lives

Mathdle treats 2 × (3 + 4) and 2 × 3 + 2 × 4 as different expressions, even though they evaluate to the same value. This is the single biggest mechanic to internalise, because every multiplicative expression you find has a distributed cousin waiting to be submitted.

The reverse — factoring a sum back into a product — is just as good. 14 + 21 and 7 × (2 + 3) are two points instead of one. On Hard and Impossible boards, factor and distribute every product you discover. You will roughly double your score with no new ideas.

What does not count as a new expression:

• Reordering inside a + chain or a × chain.
• Reparenthesising inside the same operator chain. (2 + 3) + 4 and 2 + (3 + 4) are the same.
• Identity operations. x + 0, x × 1, and on Impossible x^1, 1^x, x mod 1, √1, 0!, 1!, 2! are all rejected as trivial.

Hunting the pangram

A pangram uses all seven tiles in one expression and earns a +7 bonus on top of its tile points. There is almost always at least one pangram per puzzle; on most boards there are several.

Pangram hunting strategies that consistently work:

• Pair into the target, then bridge. If two pairs of tiles each sum to the target, you can subtract one from the other and add the remaining tiles back in a way that nets to zero. A common shape: (a + b) + (c − c) + (d × e ÷ d ÷ e) reduces, but the engine rejects identities, so the bridging tiles have to do real work. Look for two tiles that multiply or divide back into a useful constant.
• Use the center as the pivot.The center tile is mandatory in every expression, so make it the structural backbone. If the center is a large number, your pangram probably revolves around dividing or subtracting away from it. If it's small, your pangram probably multiplies it up.
• Spend the awkward tiles first.Every board has one or two tiles that don't play well — a 1, a 7, a prime that doesn't divide the target. Commit those into the expression first, then build the remaining skeleton around what's left.
• Distribute your pangram for a second one. If you find a pangram with a multiplication, try distributing it. The distributed form is a separate pangram in the catalogue and earns its own bonus.

Impossible mode: the four extra operators

Impossible adds mod, √, ^, and !. Each one opens up a different family of constructions; if you ignore them you cap out well below Euler.

• Factorial (!) is the most explosive. 5! = 120, 6! = 720, 7! = 5040. If the target is a large round number, a factorial somewhere in the expression is often the cheapest path. Factorials are restricted to non-negative integers up to 8.
• Square root (√) is the most surgical. It only accepts perfect squares (√49 = 7, √4 = 2), so it shrinks a tile that's otherwise hard to spend. If you have a 16 or 25 or 36 that doesn't fit into your target cleanly, root it.
• Exponent (^) is capped at magnitude 4 to keep numbers sane. Good for producing 8, 16, 27, 32, 64, 81. If the target is a power, look for the base and exponent pair in your tiles directly.
• Modulo (mod) is the wildcard. x mod y is the remainder of integer division. Use it to shave a tile down into a small residue. If the target is 2 and you have a 17 and a 5, 17 mod 5 = 2is a clean win.

Tier strategy

Ranks rise through eight tiers: Start, Warming Up, Good, Solid, Nice, Amazing, Genius, Euler. Genius is awarded at a fixed point threshold (roughly 70% of the catalogued total). Euler requires finding every catalogued expression — including the awkward ones nobody intuits, which is why it's rare.

Practical tier targets:

• Solidis reachable in 5–10 minutes on Easy and Medium with just the “cheapest hits” loop above.
• Genius on Hard typically requires finding at least one pangram and being deliberate about distribution.
• Euler on Impossible is a serious puzzle. Expect to revisit the board across the day. Use the glossary if you're unsure whether an expression is canonical.

Habits that compound

• Write down candidates.When you spot an expression but aren't sure it's canonical yet, type it in. The engine will tell you instantly. Faster than reasoning about it in your head.
• Use the keyboard. Digits, +, -, *, /, (, ), and Enter all map directly to the board. Power users solve faster with the keyboard than with taps.
• Trust the streak freeze.Miss a day and your streak survives automatically. Don't panic-play at midnight UTC.
• Pick a difficulty that matches your mood. Easy and Medium are meant to be 5-minute puzzles. Hard and Impossible are meant to live in the back of your head all day. Both are valid.

For the exact rules the engine uses to canonicalise expressions, see the math behind Mathdle. For definitions of pangram, tier, identity, and friends, see the glossary.