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Multiplication Magic

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.

N000ughty Thoughts

How many noughts are at the end of these giant numbers?

DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

There's Always One Isn't There

Age 14 to 16
Challenge Level

Take any pair of numbers, say 9 and 14.

Take the larger number, 14, and count up by that amount :


Then divide each of the values by 9, your chosen smaller number, and look at the remainders.

Notice there's a one.

Now do the same again but using different numbers, say 7 and 12.

Counting in twelves and dividing each result by 7 :

Again somewhere in those remainders is a one.

Pick the pairs how you like, somewhere there'll always be a one - won't there?

What actually happens?

Why?