Multiplying three consecutive even numbers gives 87*****8, where each "*" stands for a digit. What are the missing numbers?

52660 from multiplying 442, 444, 446

To have 8 digits for the product of three consecutive even numbers, the numbers would have to be three-digits.  The only triples of the last digits of three consecutive even numbers resulting in 8 is (2,4,6).  If the first digits were 3 then, the product of the three numbers would be strictly less than 64000000, if it were 5 then, the product would have 9 digits.  So the first digit is 4.  43x43x43 = 79,507 and 45x45x45 = 91125 so try 44x44x44 = 85184.  Closest to the 87000.  So the triples would be 442, 444, 446 then the product would be 87,526,608 and the answer is 52660

 

Posted by doremi on 2004-10-29 20:23:52