Make exactly

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Attempts:

Your tray

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How to play Changely

Changely is a free daily maths puzzle. Everyone gets the same five token values and the same amount each day, and your job is to make that amount exactly using as few tokens as possible. It looks simple, but the token values are chosen so the obvious approach often isn't the best one.

How the puzzle works

Tap a token to drop it into your tray. You can use any value as often as you like, and your tray shows the running total. Every puzzle is solved in advance to find its par, the fewest tokens that make the amount, and your tray holds par + 1 tokens. Make the amount exactly within that and you've solved it. Do it with exactly par tokens for a perfect ⭐. If your tray fills up, or you press Submit, you'll see how far over or under the amount you were. You get two undos a day to take a token back out, and Clear empties your tray but uses up an attempt. These are plain numbered tokens, not any real currency.

Scoring and the helper

You have six attempts. Solving it on your first attempt earns 12 points, then 10, 8, 6, 4 and 2 for attempts two to six. Each miss tells you how far away you were. Stuck early on? The helper shows one token that belongs in a best tray, but it halves the day's score and is only available during your first three attempts.

Streaks and badges

Your play streak counts the days in a row you've played, and your solved streak counts the days in a row you've solved the puzzle. Play seven days running and you earn a 7-point bonus, or 14 points if you solved all seven. Miss a day and the streaks start again. A new puzzle arrives every day at midnight UTC.

Tips

Don't just grab the biggest token. A few middle-sized ones often beat one big one plus lots of small change.

Try dividing the amount by each token value: an exact or near-exact fit is a strong hint.

Undos are precious: you get two a day, shared across all your attempts. Save them for a genuine slip.

What Changely trains

Mental arithmetic. Adding up token values quickly and accurately.

Optimising. Finding the fewest tokens, not just a combination that works.

Testing ideas. Checking whether the obvious approach really is best.

Did you know?

Always taking the biggest coin first is called a greedy algorithm. With unusual coin values it doesn't always give the fewest coins: with coins of 1, 3 and 4, it makes 6 as 4 + 1 + 1, but 3 + 3 is better.

Australia withdrew its 1 and 2 cent coins in 1992.

Your attempts