Problem | Teachers' Notes | Hint | Solution | Printable page |

Take a four-digit number: $3527$
Move the first digit to the 'back of the queue' and move the rest along, giving $5273$

Now add your two numbers.

I'm told that this process is supposed to generate numbers with a particular property.
What properties does your total have that might be the one we're after?

Now try $6154$. Then try $4139$, and a few other four-digit numbers.
What do all your answers have in common?

Does this always work for four-digit numbers? Why?

Check that it works for other numbers, two-digit, three-digit, five-digit, 38-digit...

Can you explain your findings?

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Factors and multiples. Workshop. Number operations - generally. Place value. Disproof by counterexample. Creating expressions/formulae. Mathematical reasoning & proof. Manipulating algebraic expressions/formulae. Divisibility. Generalising.