17. The Knave of Hearts stole some tarts. He ate half of them, and half a tart more. The Knave of Diamonds ate half of what was left, and half a tart more. Then the Knave of Clubs ate half of what remained, and half a tart more. This left just one tart for the Knave of Spades.
How many tarts did the Knave of Hearts steal?
A 63
B 31
C 19
D 17
E 15
17. E Suppose that at a particular stage there are $m$ tarts available for a Knave to eat and that there are $n$ left after he has finished eating.
Then $n=m-\left(\frac{1}{2} m+\frac{1}{2}\right)=\frac{1}{2} m-\frac{1}{2}$.
Therefore, $m=2 n+1$.
As the Knave of Spades received one tart, then the number of tarts which the Knave of Clubs was given was $2 \times 1+1=3$.
Similarly, the number of tarts which the Knave of Diamonds was given was $2 \times 3+1=7$.
Finally, the number of tarts which the Knave of Hearts stole was $2 \times 7+1=15$.