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Try a puzzle first, then open the hint if you need a nudge. The answer is there when you are ready.
Pick any number, then:
Try it with three different numbers. What do you notice, and can you explain why?
Call your starting number n and write each step as an expression.
You always finish with 3. Starting with n: double it to get 2n, add 6 to get 2n + 6, halve it to get n + 3, then take away n and 3 is left.
The sum of five consecutive whole numbers is 85.
What are the five numbers? Can you find them without trial and error?
The middle number is the average of all five.
85 ÷ 5 = 17 is the middle number, so the numbers are 15, 16, 17, 18 and 19.
Take a two-digit number, reverse its digits, then add the two numbers together.
Try 47, 23 and 68. Why is the answer always a multiple of 11?
Write the number as 10a + b, where a is the tens digit and b is the units digit.
The number is 10a + b and the reversed number is 10b + a. Added together they make 11a + 11b, which is 11(a + b), so it is always a multiple of 11.