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    Take any positive whole number not greater than 50. If the number is even, divide it by two. If the number is odd, multiply it by 3, and add 1 to the result. Apply the same method to the resulting number, and continue in this way forming a chain of numbers untill you finally arrive at the number 1.Shown below is a chain of numbers that results from this method if you begin with 15: 15 - 46 - 23 - 70 - 35 - 106 - 53 - 160 - 80 - 40 - 20 - 10 - 5 - 16 - 8 - 4 - 2 - 1. As you can see, the number 15 requires 17 steps to end up at 1. Of the numbers not greater then 50, which takes the longest to reach the number 1?

    Question #23808. Asked by Domonic.

    Barrow boy

    		27 which requires 111 steps.

    Nov 02 02, 1:59 PM
    Domonic

    		Barrow is correct.
    Do all numbers eventually arrive at 1 using this method? Certainly all the numbers that have been tested do, but no general proof is known that it is true for all numbers. As the Hungarian mathematician Paul Edros said: 'Mathematics isn't ready for that sort of problem.'

    Nov 02 02, 4:09 PM

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