Henry Ernest Dudeney/Modern Puzzles/207 - The Twenty-Two Game
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Modern Puzzles by Henry Ernest Dudeney: $207$
- The Twenty-Two Game
- Here is a variation of our little "Thirty-one Game" (The Canterbury Puzzles: No. $79$).
- Lay out the $16$ cards as shown.
$\qquad \begin{matrix} \boxed {A \heartsuit} & \boxed {A \spadesuit} & \boxed {A \diamondsuit} & \boxed {A \clubsuit} \\ \boxed {2 \heartsuit} & \boxed {2 \spadesuit} & \boxed {2 \diamondsuit} & \boxed {2 \clubsuit} \\ \boxed {3 \heartsuit} & \boxed {3 \spadesuit} & \boxed {3 \diamondsuit} & \boxed {3 \clubsuit} \\ \boxed {4 \heartsuit} & \boxed {4 \spadesuit} & \boxed {4 \diamondsuit} & \boxed {4 \clubsuit} \\ \end{matrix}$
- Two players alternately turn down a card and add it to the common score,
- and the player who makes the score of $22$, or forces his opponent to go beyond that number, wins.
- For example, $A$ turns down a $4$, $B$ turns down $3$ (counting $7$), $A$ turns down a $4$ (counting $11$),
- $B$ plays a $2$ (counting $13$), $A$ plays $1$ (counting $14$), $B$ plays $3$ ($17$), and whatever $A$ does, $B$ scores the winning $22$ next play.
- Now, which player should always win, and how?
Click here for solution
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Puzzle Games: $207$. -- The Twenty-Two Game
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Game Puzzles: $476$. The $22$ Game