

The 421 Loop - mquaes

A Math-magical Loop 
Pick a whole number and enter it into your calculator.<p><pre><code>    If it is even, divide by 2. If it is odd, multiply by 3 and add 1.
    Repeat the process with the new number over and over. What happens?
    The sequence always ends in the "loop": 4.....2.....1.....4.....2.....1...
</code></pre>
Let’s illustrate with an Example:<p>Start with 17
17 is odd, so we multiply by 3 and add 1. We get 52. (17x3=51+1=52)
52 is even, so we divide by 2. We get 26. (52 / 2 = 26)
26 is also even, so we divide by 2 again and get 13.
13 is odd, so we multiply by 3 and add 1. We get 40. (13x3=39+1=40)
40 is even, so we divide by 2. We get 20. (40 / 2 = 20)
20 is even, so we divide by 2 and get 10.
10 is also even so we divide by 2 again and get 5.
5 is odd so we multiply by 3 and add 1. We get 16.
16 is even, so we divide by 2 and get 8.
8 is also even so we divide by 2 again and get 4.
4 is even so we divide by 2. We get 2.
2 is even, so we divide by 1 and get 1.
1 is odd, so we multiply by 3 and add 1. We get 4.
4 is even so we divide by 2. We get 2. And so we begin the loop
4.....2.....1.....4.....2.....1...
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mquaes
<http://mathema-tricks.blogspot.com/>

