Factorial With All Of The Digits!

Computer Science Level 3

What is the smallest non-negative integer n n for which n ! n! starts with the digit 9?


The answer is 96.

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Vishnu Bhagyanath by Vishnu Bhagyanath , 23, India

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5 solutions 

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def fact(n):
    ans = 1
    while n>0:
        ans *= n
        n -= 1
    return ans    

n = 2
while True:
    temp = str( fact(n) )
    if temp[0] == '9':
        print n
        break
    n += 1

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Here 's a C++ solution using a mathematical approach which is that the first digit of a positive integer n n is given by,

First digit ( n ) = ⌊ 1 0 { log ⁡ 10 ( n ) } ⌋ \large\textrm{First digit }(n)=\left\lfloor 10^{\{\log_{10}(n)\}}\right\rfloor

where { ⋅ } \{\cdot\} is the fractional part function and ⌊ ⋅ ⌋ \lfloor\cdot\rfloor is the floor function . Proving the above claimed formula is quite easy (using basic exponent laws and logarithm laws) and is left as an exercise to the reader.

Prasun Biswas - 5 years, 10 months ago
Bill Bell
Sep 16, 2015

Calculating factorials is expensive, and so is converting integers to strings. I therefore avoided both of these calculations. (Not that it matters in this case!) 

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def biggest_digit(n):
    while n>=10:
        n = n / 10
    return n

n=1
f=1
while True:
    n+=1
    f*=n
    if biggest_digit(f)==9:
        print n
        break

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ícaro Augusto
Aug 19, 2015

Ruby 

def factorial(n)
  i = n
  until (i == 1) do
    i -= 1
    n = n * i
  end
  n
end



x = 0
h = 0
while x == 0 do
  h += 1
  a = factorial(h).to_s
  if a[0] == "9"
    x = 1
  end  
end

puts h
gets.chomp
1 Helpful 0 Interesting 0 Brilliant 0 Confused
Arulx Z
Aug 6, 2015 
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>>> import math
>>> n = 1
>>> while str(math.factorial(n))[0] != '9':
        n += 1
>>> print n

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Simple standard approach.

I have a mathlab/octave solution for those who are interested :

clear all;

format long

number = 0;

for i = 1 : 170 

number = factorial(i);

do 

number = number/10;

until (number <10)

if (floor(number) == 9)

disp ("The wanted number is :"), disp (i)

break;

endif

Tom Van Lier - 5 years, 10 months ago
Aareyan Manzoor
Aug 30, 2015

python 3 . returns 96

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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