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avatar+106 

William writes the integers from 2 through 15 from left to right on a piece of paper, then does the following:


* He begins by circling the leftmost uncircled integer, then circles all its powers. Afterwards, he repeats this process until every integer is circled.
* Then he crosses off the rightmost uncrossed integer, then crosses off all even numbers less than it in decreasing order. Afterwards, he repeats this process until every integer is crossed off.

Find the product of the last integer William circled and the last integer William crossed off.

 
 Oct 22, 2025
 #1
avatar+2264 
+1

 

Last circled, 15     

Last crossed off, 3     15 x 3 = 45     

.     

 Oct 23, 2025
 #2
avatar+37184 
+1

He first circles '2'    then circles the powers of 2 :  cirlces 4   circles  8  

He then circles '3'   then circles the powers of 3 :  circles 9 

He then circles '4'    no powers of 4 are on the list so no circles   and :

He then circles 5    then 6  ,7  ,10 ,11, 12 , 13 , 14  and lastly   '15 '

 

Now, he starts crossing:

   He  crosses off 15    then 14 , 12, 10 , 8 , 6, 4, ,2

    He then crosses off 13    then crosses off 11 , 9 ,7,5,and lastly '3'   

 

Last circled = 15     last crossed = 3           3 X 15 = 45 

 Oct 24, 2025

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