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The Ackermann function can be defined as follows: \[ A(m,n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. \end{cases} \]

What is the value of \( A(3,6)? \)

If his bottles have the following masses, and he can carry as many of each as he likes (so long as the total is less than or equal to 15 kg), what is the most amount of water that Tom can carry?

- Tiny: 0.77 kg
- Small: 1.10 kg
- Medium: 3.4 kg
- Large: 7 kg

Compute the number of paths from S (start) to G (goal) in the following image, without using any road twice (but may visit an intersection twice). As an explicit example, the path in pink is one valid path.

**Clarifications:**

- A road is a segment between two intersections that doesn't include any other intersection. A path is a connected sequence of roads from start to goal.

\[1,2,3,4,5,6,7,8,9\]

in a \(3 \times 3\) matrix, how many configurations are there such that all lines (rows, columns and diagonals) add up to the same sum?

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