SOLUTION: A list of whole numbers from 1 to 2015 is written on a sheet of paper. All the multiples of 5 are then struck off from the list. What is the last digit of the product of the remain

To get the answer, we should look and trace the last digit, only.


Regarding last digits, for our first numbers 1, 2, 3, 4, , 6, 7, 8, 9,  the last digit of the product is


    1*2*3*4*6*7*8*9 = 6 (mod10)   <<<---===  I wrote the LAST digit only (!!!)


Now, these factors will be cyclically repeated for every 10 numbers (with excluded 5 and 0).


Therefore, the last digit of the product, created by every 10 numbers, is 6.


    6*6 = 36 = 6 (mod10),


therefore, the last digit of the product of all these factors from 1 to 2010 (with excluded multiples of 5) is 6.


Now, to answer the final question, we should calculate

  
    6 * 11*12*13*14.


or, tracing the last digit only,  the product


    6 * 1*2*3*4 = 4  (mod10).


ANSWER.  The last digit of the number under the question is 4.