Candice feels the power!

Candice scratched her head and finally found a solution to the question posed by the cashier. Having solved so many mathematics questions, she feels she has enough knowledge on the subject and decides to show off in front of someone.

On her way back with a box full of beverage cans, she spots a random man in an overcrowded street. She decides to boast of her mathematical skills and tells the man : "I can solve any mathematics problem in the world! If you don't believe me, ask me anything! ".

Unfortunately, Candice did not realize that this man was a skilled Number Theorist ! He replies : "All right then, I am thinking of a number. The sum of the digits of this number, raised to the number of digits of this number produces this very number itself. What number am I thinking of?". He adds, "To make things simpler, this number has as many digits as the number of primes between 310 310 and 320 320 ."

Candice appears dumbstruck and can't get through this question alone. Can you help Candice find this number?

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Check out Candice's Other Adventures!


The answer is 512.

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1 solution

Subhiksha Nd
Sep 3, 2015
  1. Basic hint: 311, 313, and 317 are the prime numbers between 310 and 320.. ( 319= 29*11) So, the required number has 3 digits. (And each digit is less that 10.)
  2. The next thing is sum of the digits, when "CUBED" gives the number.
  3. Only the cubes of 5 to 10 has 3 digits!! (This narrows down of trials)
  4. 5^3= 125. But 1+2+5=8( not equal to 5). Similarly, try for 6 and 7.
  5. 8^3=512. 5+1+2=8....

Yay! So the required number is 512, and it satisfies all conditions!!

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