Do the trick. Ask someone to write a number of three or four digits, mix the digits into any order, and take the smaller from the bigger. They circle one digit that is not zero and read you the rest. Add up what they read. The hidden digit is whatever it takes to reach the next multiple of nine.

Before chapter 4. Why won't the trick work if you hide a zero?

The answer. If the hidden digit is 0, the digits that are left already add to a multiple of nine, and so they would if the hidden digit were 9. The trick cannot tell the two apart. Every difference in the book (2727, 3087, 5175) has digits adding to 18, because a number and its mix leave the same remainder after dividing by nine, so their difference leaves none.

The grown-up layer. This is the idea behind "casting out nines", an old way to check sums. ShowMath has Missa; MentalForge has Nina, who uses nines to check her working.

Pause to think. Beto said the zero rule was cheating. Was it?

For the ride home. Ask: what do the digits of 9, 18, 27, 36 and 45 add up to?