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Here's a trick. Pick a two-digit number. Reverse its digits: write them backwards. Subtract the smaller number from the bigger. The answer can be named before you say it — every time.

Number Play — finding patterns in numbers, then testing, proving or breaking them. You will meet parity, which means odd or even. You will also meet grids, number sequences and digit puzzles. First, why does the trick above work?

What this track covers

• Digit sums — add the digits. Divide a number and its digit sum by 9. The leftovers match. The same holds for 3.
• Why it works — the real reason behind that trick.
• Odd times even. A product is the answer to a multiplication. A product is odd only when both numbers are odd.
• Reverse and subtract — a Kaprekar round. Make the biggest and smallest number from the digits. Subtract. The trick is proved for every two-digit number.
• Many clues — clues used together to find a number.
• When it stops — one bad case can break a claim. A Collatz path shows a claim that has not broken yet.
• Saying why — putting a reason in an order that works.
• Odd and even, added. Count the odd numbers. That count decides the sum.
• Magic squares. Rows, columns and diagonals all add to the same sum. That sum is the magic sum. The magic sum is 3 times the centre.
• Counting rhythms. Count rhythms made of short and long beats. The counts are 1, 2, 3, 5, 8.
• Letters for digits. Solve a letter puzzle. Start at the units column, the ones place.
• Even or odd expressions. Here n is any whole number. 2n is even. 2n − 1 is odd.

Quick catch-up

These earlier lessons help you here.

• Place value (Track Zero). Where a digit sits decides what it is worth.
• Divisibility tests (Prime Time). Quick checks for 2, 3, 5, 9 and 10.
• Odd and even (Patterns) — even numbers pair up. Odd numbers leave one over.
• A rule is not a proof (Patterns). Three matching numbers are a start. They are not a proof.