x = 1! + 2! + 3! + 4! + ... + 100!. What is the unit's digit of
(x^)x^ x^ x........?

a. 3
b. 1
c. 7
d. 0
e. Can't be determined.

• 1!=1
  2!=2
  3!=6
  4!=24
  5! onwards all end with 0...
  unit digit=1+2+6+4=13
  unit digit=3
• 9 years agoHelpfull: Yes(33) No(15)
• 1+2+6+4=13,unit digit of x is 3.
  so,(3^)3^3^3=(7^)3^3=3^3=7
  ans.is 7
• 9 years agoHelpfull: Yes(20) No(6)
• ans is (e)
  because 3 is the unit place of x
  but we have to find (x^)x^x^........
  so we don't know what's the power of x exactly
  hence can't be determined
• 9 years agoHelpfull: Yes(10) No(1)
• after 5! the factorials end with 0 therefore sum upto 4! is 33 therefore the unit digit is 3 now(3)^3^3^3..... =? 3^3=27^3 the unit digit is 1^3 is 1 therfore the ans is 1
• 9 years agoHelpfull: Yes(3) No(4)
• ans-d)0
  x=1+2+6+4+0+0 all aftr 5! all unit digit 0.so now x=13 so unit digig 3.
  Then 3^3^3^3^... =we have to calculate unit digit so we must divide the fst power i.e 3^(3/4)^3^3^3^..... so nw 3/4 means -1 & (-1)^odd means -1.
  now 3^(-1)=0.so unit digit also 0.
• 9 years agoHelpfull: Yes(3) No(5)
• answer is 3,... because 1! +2! +3! +4! gives u 33.. n from 5! zero strats... so it will be 3
• 9 years agoHelpfull: Yes(2) No(0)
• It's true that x = 3
  But we don't know how many powers x has been raised.
  So the possible values when 3 is raised to any power is 1,3,9.
  So answer can't be determined.
• 9 years agoHelpfull: Yes(2) No(0)
• Last digit of x will be 3(1+2+6+24) since after 5! factorial of every number gives a result that ends with zero.
  
  Now 3^3 gives the last digit 7. 7^3 gives a last digit 3.
  
  the last digit of (3^)3^3^3......is either 3 or 7
  
  answer: cannot be determined.
• 9 years agoHelpfull: Yes(2) No(0)
• after 5! every factorial must contain 0 so it shuld be 3
• 9 years agoHelpfull: Yes(1) No(0)
• Can't be determined
• 9 years agoHelpfull: Yes(1) No(3)
• 1!=1,2!=2,3!=6,4!=24,5!=120,6!=720............
  1+2+6+24+120....=units digit=3
• 9 years agoHelpfull: Yes(1) No(0)
• cant be determined
  
• 9 years agoHelpfull: Yes(1) No(0)
• unit digit is 3
• 9 years agoHelpfull: Yes(1) No(0)
• may be 0.it's guessed
  
• 9 years agoHelpfull: Yes(0) No(7)
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• 9 years agoHelpfull: Yes(0) No(0)
• karthikeyank sir explain ans to dis question
  
• 9 years agoHelpfull: Yes(0) No(0)
• 1 is the correct ans because 81/10=1 so 1 is repeated
• 9 years agoHelpfull: Yes(0) No(0)
• Ans should be 1
  since x^(x^x^x^x^x^x^....) should be in the form of x^(3n)
  so x/3n rem=0
  hence x^o=1
• 9 years agoHelpfull: Yes(0) No(1)
• ans:0 since the whole number will b multiple of 100
• 9 years agoHelpfull: Yes(0) No(1)
• unit digit of 1!+2!+3!.....+100!=3,then 3^3^3^3^.....=
  (3^3)^3^3...=
  1^3^3...= unit digit is 1,because it will keep on repeating..ans is B
• 9 years agoHelpfull: Yes(0) No(1)
• Here if we break factorial than it becomes as
  =1+2+6+24+120+720+....in all last digit will be one so
  We count
  =1+2+6+4=)13
  So last unit digit will be 3 .
  Ans a
• 9 years agoHelpfull: Yes(0) No(0)
• when we add 1!+2!+3!+....+100! the last four digits will be 0.So if you take the value for x as same from the question you will get 0 in the units digit.
  Option d
• 9 years agoHelpfull: Yes(0) No(1)
• Observe x = 1! + 2! + 3! + .... + 100!.
  The X value ends with 13.
  divide 13 by 4 remainder will be 1.
  So the last digit of the given expression will be 3.
  Ans is 3.
• 9 years agoHelpfull: Yes(0) No(0)