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N=1991*1993*1995*1997*1999*2001*2003*2005*2007 What is the sum of the hundreds, tens and units digits of N?

 Jan 6, 2022
 #2
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N=1991*1993*1995*1997*1999*2001*2003*2005*2007, solve for N

 

N = 509685296446883641136997950775

 

7  +  7  +  5 ==19

 Jan 6, 2022
 #3
avatar+115924 
+1

Now without a calculator:

 

1991*1993*1995*1997*1999*2001*2003*2005*2007  (only care about last 3 digits)

 

same as

(2000-7)(2000+7)(2000-5)(2000+5)(2000-3)(2000+3)(2000-1)(2000+1)(2000-9) mod1000

= (1000-49)(1000-25)(1000-9)(1000-1)(1000-9)  mod 1000

= (-49*-25*-9*-1*-9)  Mod1000

= -(49*25*81)   mod1000

= -(49*25*80+49*25)   mod1000

= -(49*2000+49*25)   mod1000

= -(49*25)   mod1000

= -(40*25+9*25)   mod1000

= -(9*25) mod 1000

= -225 mod 1000

= 1000-225  mod1000

= 775 mod 1000

 

7+7+5 = 19

 Jan 11, 2022

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