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Janice gave me a calculator with a special button marked * This button behaves weirdly: When an odd integer is displayed, pressing the * button multiplies the number by 3 and then subtracts 1 When an even integer is displayed, pressing the * button divides it by 2 If this calculator displays the number 5 now, what will it display after I press the * button 1001 times?

 Nov 18, 2020
 #1
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Let's see if we have a repetitive pattern

 

Beginning number         Ending number                           

             5                           14

            14                           7

             7                          20

             10                          5   

              5                          14    ........              

      

 

Note  that  the cycle starts over after every 4 steps

 

After pressing the button 1000 times   (since 1000 is divisible  by 4)   we are back at 5

 

Pressing the button on the 1001th time will display  5*3 - 1  =   14

 

cool cool cool 

 Nov 19, 2020

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