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# Pablito's Solitaire

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Pablito's Solitaire is played with checkers situated on a trianglular board of hexagons. In this picture the o's denote hexagons and -, /, and \ denote adjacencies.
```                    o
/ \
o - o
/ \ / \
o - o - o
/ \ / \ / \
o - o - o - o
/ \ / \ / \ / \
.........
```
You are to place as many pieces as desired at or below a given row R, and you are to jump and remove pieces as in checkers. Your goal is to reach the top of the board. What is the largest R (lowest level on the board) from which you can reach the top?

Examples: Here are solutions for R = 1 and R = 2. I have placed an x where a checker is needed. I hope that the moves are obvious.

R = 1: using two pieces and one jump

```row 0               o
/ \
row 1             x - o
/ \ / \
x - o - o
/ \ / \ / \
```

R = 2: using three pieces and two jumps

```row 0               o
/ \
row 1             o - o
/ \ / \
row 2           x - x - o
/ \ / \ / \
o - o - x - o
```

Source: This problem was suggested by Pablo Guerrero Garcia (Universidad de Malaga, Spain). It is a variation on John Conway's "Solitaire Army."