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Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

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Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Always a Multiple?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

First video:

Charlie said: "Alison, think of a two-digit number. Reverse the digits and add your answer to your original number. I bet your answer is a multiple of 11."

Alison chose 42, added 24 and got the answer 66: "It is! How on earth did you know that?"

Charlie said: "I'm not sure. Let's try to work it out."

Second video:

Alison arranged multilink to show four tens and two units for 42, and two tens and four units for 24.
She then put the four units with the four tens, and the two units with the two tens, giving six lots of eleven.

Charlie imagined a two-digit number $ab$, where $a$ represents the number in the tens column, and $b$ respresents the number in the units. This can be written as $10a+b$. Similarly, $ba$ can be written as $10b+a$.

Charlie added these together to get $11a+11b$, which he wrote as $11(a+b)$.