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?