The game Hex was invented by the Danish mathematician Piet Hein in the 1940s. This game has been of great interest to mathematicians around the world since its introduction, including Martin Gardner who explores it in chapter eight of his first Scientific American Book of Mathematical Puzzles and Games (1959). The game is normally played on a board of 11x11 hexagons with two edges labelled black and the other two labelled white. It is a two-person game in which both players (using black and white counters) attempt to create a chain connecting both of their respective sides of the board. This chapter will stray away from the basics of Hex and instead explore a more specific aspect of the game: ladders. Topics to be discussed include general
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Shown in figures six, seven and eight is a ladder formation similar in nature to the bottleneck, in which red plays directly in between both blue counters (D4), ultimately forcing the defender to create a ladder. However, this is not done until an escape piece is first played beyond the origin of the ladder; in this case, it is placed in the fourth row. As shown in figure seven, a counter is played in D7, which blue is tricked into defending by placing a counter in F8. The ladder is ultimately formed and red is able to gain control of the edge as a result of the ladder escape, and ultimately win as shown in figure eight. Although this is a fourth row ladder escape, it is still able to guarantee a connection to the lower edge because there are no blue counters hindering the escape piece’s template. Ladder escapes placed in rows r>4, however, are not guaranteed the same success as they are essentially in the middle of the hex board and can therefore be blocked if countered correctly. Keep in mind that ladders will rarely form more than four rows away from an …show more content…
Ladder escape foils are counters placed near ladder escapes that enable the defender to prevent the escape from being successful. Browne explains that in order to do this, the counter must either somehow interfere with the escape piece’s template (empty spaces connecting it to the edge) or actually block the ladder’s intended path (Browne 2000). Ladder escape foils will often be placed unintentionally earlier in the game, but their importance becomes apparent if the ladder forms in the correct place relative to it. For the example shown in figure nine, the ladder escape foil doesn 't block the ladder’s intended path, however it does interfere with the template and a potential bridge. In this case, the counter that will ultimately lead to the foiling of the escape is the one placed at C4 (highlighted in yellow), directly adjacent to blue’s ladder escape at C3. Because of this adjacency, these foils are referred to as adjacent move foils (Browne 2002). As it is now red’s turn, two possible moves can be made that foil the ladder escape and ensure a victory for red, can you find
Shown in figures six, seven and eight is a ladder formation similar in nature to the bottleneck, in which red plays directly in between both blue counters (D4), ultimately forcing the defender to create a ladder. However, this is not done until an escape piece is first played beyond the origin of the ladder; in this case, it is placed in the fourth row. As shown in figure seven, a counter is played in D7, which blue is tricked into defending by placing a counter in F8. The ladder is ultimately formed and red is able to gain control of the edge as a result of the ladder escape, and ultimately win as shown in figure eight. Although this is a fourth row ladder escape, it is still able to guarantee a connection to the lower edge because there are no blue counters hindering the escape piece’s template. Ladder escapes placed in rows r>4, however, are not guaranteed the same success as they are essentially in the middle of the hex board and can therefore be blocked if countered correctly. Keep in mind that ladders will rarely form more than four rows away from an …show more content…
Ladder escape foils are counters placed near ladder escapes that enable the defender to prevent the escape from being successful. Browne explains that in order to do this, the counter must either somehow interfere with the escape piece’s template (empty spaces connecting it to the edge) or actually block the ladder’s intended path (Browne 2000). Ladder escape foils will often be placed unintentionally earlier in the game, but their importance becomes apparent if the ladder forms in the correct place relative to it. For the example shown in figure nine, the ladder escape foil doesn 't block the ladder’s intended path, however it does interfere with the template and a potential bridge. In this case, the counter that will ultimately lead to the foiling of the escape is the one placed at C4 (highlighted in yellow), directly adjacent to blue’s ladder escape at C3. Because of this adjacency, these foils are referred to as adjacent move foils (Browne 2002). As it is now red’s turn, two possible moves can be made that foil the ladder escape and ensure a victory for red, can you find