The Power-Dice System

In Challenge and Expert three of your seven dice are coloured, and each one demands to be used with a particular kind of operation. Satisfy two and your solve is Valid. Satisfy all three and it is Perfect.

The three colours

A Challenge or Expert board looks like this — four plain white dice and the three coloured ones:

What each die demands

Green — must be added or subtracted. Use it with + or −.

Blue — must be multiplied or divided. Use it with × or ÷.

Red — must take part in a power. Use it as the base or as the exponent, with ^.

The other four dice are white and carry no requirement at all. Use them however the arithmetic needs.

Use at least two of the three correctly and the solve counts as Valid. Use all three and it is a Perfect solve, which is what earns a Puzzle Piece in the Daily Challenge. In Expert mode the bar is higher: only a Perfect solve counts at all.

Place them in order of difficulty

The three colours are not equally hard to satisfy, and the order you place them in decides how often you finish Perfect. Work from most-constrained to least:

Red first. An exponent is by far the fussiest thing to fit — it changes magnitude violently and there are only a few powers that land usefully near 37. Build your equation around it.
Blue second. Multiplication is flexible, but it still needs a partner and it still scales your total.
Green last. Adding or subtracting fits almost anywhere, so the green die is the one you can nearly always place at the end.

Players who go the other way — greedily placing green because it is easy — routinely end up with a red die and nowhere sensible to put it. That is the difference between a 2-of-3 Valid solve and a 3-of-3 Perfect one.

The trick that saves Perfect solves

When the red die simply will not fit as a meaningful exponent, remember that anything raised to the power of 1 is unchanged. x^1 = x. If your red die shows a 1, it can be the exponent on any term at all, changing nothing and satisfying its requirement completely.

(6×2)^1+6+4+5×3 The whole bracket is raised to the power of 1 — value untouched, red die satisfied, Perfect solve.

The mirror of the trick works too: a term you build to equal 1 can be the *base* under a red exponent, since 1 raised to anything is still 1.

(6×1)^2+3−1−6÷6 Here the red die is the exponent 2 on a bracket worth 6, giving 36 — then 3−1−1 nets +1.

What counts as correct use

The requirement is about the operation the die takes part in, not where it sits in the equation. A green die is used correctly if it is a term being added or subtracted — it does not matter whether it is first, last or inside a bracket.

1×6+2^3+4×5+3 Three separate jobs: a power, a product, and a plain added term — all three colours satisfied.

A die can only satisfy one requirement, and it satisfies the requirement of the operation it is directly attached to. A green die inside a bracket that is later multiplied is still being added *within* that bracket, which is what its colour asks for.

Where the colours appear

Easy — no power dice at all. All seven dice are white; just reach 37.
Challenge — power dice on. Two of three correct is a Valid solve; all three is Perfect.
Expert — the same power dice, judged strictly: only a Perfect solve counts. Two of three is a miss, not a lesser win.

Each of those three tiers has an untimed practice round and its own timed Daily, so the colours behave identically whether you are practising or racing the clock — only the judging and the stakes change. The modes page lays out all six.

If you are new to the colours, spend a few rounds in Challenge practice before taking them into a Daily. It is untimed on purpose.

The three mistakes that cost Perfect solves

Almost every dropped Perfect comes from one of these, and all three are avoidable once you know to look for them.

Placing green first because it is easy. It feels productive and it quietly consumes the flexibility the red die needed. Place red first, always.
Treating the red die as a big-number generator. It does not have to grow anything. ^1 satisfies it completely while changing nothing, and that is frequently the correct move.
Forgetting that the blue die can divide. Players reach for multiplication automatically, but division is the same requirement — and blue ÷ something is often the only way to fit a large blue face onto a board that is already close to 37.

If a board keeps ending in a 2-of-3, it is nearly always the red die that got stranded. Rebuild from the exponent outwards rather than trying to bolt one on at the end. There is a fuller list of pitfalls in common mistakes, and the powers themselves are covered in the exponent guide.