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Investigation time!

Today, you are going to try and make the longest and shortest halving chains that you can. 

To do this, pick a number to start with: If the number is even, halve it, if the number is odd, add 1. Keep going until you get to 1.


Start with 10.

Half of 10 is 5.

5 is odd, so I must add 1 to make 6.

Half of 6 is 3.

3 is odd, so I must add 1 to make 4.

Half of 4 is 2.

Half of 2 is 1.

I halved this 4 times.

As you work, record your results and try starting with different two-digit numbers.

Do larger numbers produce longer chains?