Henry Ernest Dudeney/Modern Puzzles/169 - The Card Pentagon/Solution

by : $169$

 * The Card Pentagon

Solution

 * Deal the cards $1$, $2$, $3$, $4$, $5$ in the manner indicated by the dotted lines
 * (that is, drop one at every alternate angle in a clockwise direction round the pentagon),
 * and then deal the $6$, $7$, $8$, $9$, $10$ in the opposite direction, as shown,
 * taking care to start with the $6$ on the correct side of the $5$.
 * ''The pips on every side add to $14$.


 * Dudeney-Modern-Puzzles-169-solution.png


 * If you deal the $6$, $7$, $8$, $9$, $10$ in the first manner and the $1$, $2$, $3$, $4$, $5$ in the second manner,
 * you will get another solution, adding up to $19$.


 * Now work with the two sets of numbers $1$, $3$, $5$, $7$, $9$ and $2$, $4$, $6$, $8$, $10$ in the same way
 * and you will get two more solutions, adding, respectively, to $16$ and $17$.


 * There are $6$ solutions in all.
 * The last two are peculiar.
 * Write in, in the same order, $1$, $4$, $7$, $10$, $13$ and $6$, $9$, $12$, $15$, $18$;
 * also write in $8$, $11$, $14$, $17$, $20$ and $3$, $6$, $9$, $12$, $15$.
 * Then deduct $10$ from every number greater than $10$.