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?
Let's see if we have a repetitive pattern
Beginning number Ending number
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