Problem
Square 1 holds one grain. Each later square holds twice as many grains as the previous square. Return both the count on the requested square and the total on squares 1 through 64. Write each count as decimal text, because the board total is too large for a signed 64-bit integer.
Implement chessboard_grains(square).
Input
square: The requested square, numbered from 1.
Output
Return two decimal strings: [count on the requested square, total on all 64 squares].
Constraints
1 ≤ square ≤ 64. Output strings contain decimal digits only, with no commas, spaces, or leading zeros.
Examples
Input:
square = 6
Expected output:
expected = ["32", "18446744073709551615"]Input:
long long square = 6;
Expected output:
std::vector<std::string> expected = {"32", "18446744073709551615"};Input:
long square = 6;
Expected output:
string[] expected = new string[] {"32", "18446744073709551615"};Explanation
The first six counts are 1, 2, 4, 8, 16, 32. The board total is 1 + 2 + … + 2⁶³ = 2⁶⁴ − 1.
Input:
square = 1
Expected output:
expected = ["1", "18446744073709551615"]Input:
long long square = 1;
Expected output:
std::vector<std::string> expected = {"1", "18446744073709551615"};Input:
long square = 1;
Expected output:
string[] expected = new string[] {"1", "18446744073709551615"};Explanation
The first square holds 1 grain. The second output always refers to all 64 squares, not just the requested prefix.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Each square doubles the previous square, so the requested count depends only on its position.
Hint 2
The total across all 64 squares is a geometric progression, and it grows far beyond normal integer limits.
Hint 3
Return both values as plain decimal text, and watch that the first square is one, not zero.
Expected complexity
O(1) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.