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The number 55 was multiplied by a 55-digit number containing only ones. What is the sum of the digits of the product?

 Mar 29, 2021
 #1
avatar+117787 
+2

Discovering a pattern is  always   a useful thing to  try in these problems

 

Note

 

55 *  11  = 605

55 *  111  =  6105

55  *  1111  =  61105

55  * 11111 =  611105

 

It  appears  that  the  sum  =  6 + 5  +  ( n - 2) * 1      where  "n"  is  the  number  of 1s we are multiplying  by

 

So...multiplying  by  55  " 1s "   gives  the  sum :   6 + 5 +  (55 - 2) ^ 1   =   11 + 53  =  64

 

 

cool cool cool

 Mar 29, 2021
edited by CPhill  Mar 29, 2021
 #2
avatar+158 
+1

Hey there, Guest!

 

So for this problem, we can actually do it in a simple way with smaller numbers:


55*11 = 605
55*111 = 6105
55*1111 = 61105
55*11111 = 611105


Do you see the pattern now?

Therefore: 6+(55-2)+0+5 = 64

 

Hope this helped! :)

( ゚д゚)つ Bye

 Mar 29, 2021

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