Hide and seek with Spiderman(The previous answer was wrong)Number Theory Level 3
There are 500 windows in a building and Spiderman knows that behind one window, there is a villain. Spiderman labelled each window from 1-500 and using his Spider Senses, received hints to which window the villain is hiding behind. The following are the hints he received:
The number comprises three digits.
The number is a prime number in a prime position.
The number has a digital sum of 11.
The square of the number has six distinct digits.
From these hints, find out which window is the villain hiding behind
- A prime number in a prime position is where you label each prime in their order. For example :
1st - 2
2nd - 3
3rd - 5
4th - 7
If the number is in a prime position(e.g. 2nd, 3rd, llth), it is a prime in a prime position. The first prime in a prime position is therefore 3.
- A digital sum of a number is the sum of all its digits. For example, the digital sum of 532 is 5+3+2 = 10.