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Even Up

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

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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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What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

Quick Times

Age 11 to 14 Challenge Level:

$32 \times 38 = 30 \times 40 + 2 \times 8$

$34 \times 36 = 30 \times 40 + 4 \times 6$

$56 \times 54 = 50 \times 60 + 6 \times 4$

$73 \times77 = 70 \times80 + 3 \times 7$


And so on?

Verify and generalise if possible.