Introduction
There once was a wise servant who saved the life of a prince.
The king promised to pay whatever the servant could dream up.
Knowing that the king loved chess, the servant told the king he would like to have grains of wheat.
One grain on the first square of a chessboard, with the number of grains doubling on each successive square.
Instructions
Calculate the number of grains of wheat on a chessboard.
A chessboard has 64 squares.
Square 1 has one grain, square 2 has two grains, square 3 has four grains, and so on, doubling each time.
Write code that calculates:
- the number of grains on a given square
- the total number of grains on the chessboard
Maximum integer value
According to the PHP docs there is a maximum integer value:
The size of an int is platform-dependent, although a maximum value of about two billion is the usual value (that's 32 bits signed).
64-bit platforms usually have a maximum value of about 9E18.
PHP does not support unsigned ints.
In other words, PHP cannot express any number 2^63 or greater as an integer.
Some of the tests for this exercise require 64 bit integers (2^64) which is beyond the integer size limitation of PHP.
PHP automatically converts ints to floats, when the numbers get too big:
If PHP encounters a number beyond the bounds of the int type, it will be interpreted as a float instead.
Also, an operation which results in a number beyond the bounds of the int type will return a float instead.
But the float type has limited precision.
And King hates unprecision.
So King decided to expect the results of the calculations as a string which expresses the integer value, rather than expressing the answer as int or float.
And he wants integer calculations, not just a lazy conversion at the end.
Can you solve this by avoiding numbers that are larger than the language will allow directly?
And please don't use other PHP libraries like gmp or bc, too.
