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Continued Multiples (Posted on 2013-11-29) Difficulty: 3 of 5
(1)Take a 2-digit number and multiply the two digits together. Repeat with each product until a single digit is the result. For most starting numbers, no more than three of these steps are needed to arrive at the final single digit. (For example: 57: 5*7=35: 3*5=15: 1*5=5). Find one that takes four steps.

(2)Start with a 3-digit number. Choose any one of the digits and remove it to make a 2-digit number. Multiply the 2-digit number by the digit you removed. Eventually, you will get a 2-digit number, which will yield a single digit, as above. What number should you start with, and what steps should you take to find the longest series of steps you can take to arrive at that final single digit

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts 1.answer 2.hint | Comment 1 of 3
1st is clearly 77 .. a common knowledge

It is too late for me to finalize the 2nd number, but I would try 
to backtrack from 77, like
 77==>171(=57*3)==>375(71*5)==>715 stop  7 steps
Hint- try to find a longer path  from 77, then try to increase the #
of steps beginning  with another #, NOT 77,49,36 OR 18.

Computer definitely gets it in no time.. 



















  Posted by Ady TZIDON on 2013-11-29 16:51:43
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