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Curious Number

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

            


Can you order the digits 1, 2 and 3 to make a number which is divisible by 3?
And when the final digit is removed again it becomes a two-digit number divisible by 2,
then finally a one-digit number divisible by 1?  

Can you order the digits 1, 2, 3 and 4 to make a number which is divisible by 4?
And when the final digit is removed it becomes a three-digit number which is divisible by 3.
And when the final digit is removed again it becomes a two-digit number divisible by 2,
then finally a one-digit number divisible by 1?

Can you order the digits 1, 2, 3, 4 and 5 to make a number which is divisible by 5?
And when the final digit is removed it becomes a four-digit number which is divisible by 4.
And when the final digit is removed it becomes a three-digit number which is divisible by 3.
And when the final digit is removed again it becomes a two-digit number divisible by 2,
then finally a one-digit number divisible by 1?

What systems are you using?
What do you know about numbers which can be divided by 3, 4, 5?
Now what about taking this further for digits 1, 2, 3, 4, 5, and 6?
What do you know about numbers which can be divided by 6, 7, 8 and 9?