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A teacher writes 6 consecutive integers on the blackboard.  He erases one of the integers and the sum of the remaining five integers is 2016.  What integer was erased?

 Dec 28, 2020
 #1
avatar+114325 
+2

Let the first digit   be  x  and the last x + 5

 

Let  a  be the sum of the constants  of the  five remaining integers

 

And we  have that 

 

5x +  a  =  2016

 

5x  =  2106 -  a

 

Notice  that    2106 - a  must be divisible  by 5

 

So   if  a =  11   we have    x + (x + 1) + ( x + 2) + (x +3)+ (x + 5)    =    5x + 11  =  2016

 

Note that x + 4 was erased...so....

 

5x   = 2016  -11

 

5x  =  2005

 

x =  401

 

So

 

x + 4  =   401 + 4   =  405   was erased

 

 

cool cool cool

 Dec 28, 2020
 #2
avatar+10824 
+2

A teacher writes 6 consecutive integers on the blackboard. He erases one of the integers and the sum of the remaining five integers is 2016. What integer was erased?

 

Hello Guest!

 

401+402+403+404+406=2016  by trying it out

laugh  !

 Dec 28, 2020
edited by asinus  Dec 28, 2020

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