Question 1183541

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?
<pre>Let original number of tarts be T
1st time around: Ate {{{1/2}}} of the tarts, and {{{1/2}}} more gives us a remainder of: {{{matrix(1,3, (1/2) * T - (1/2), "=", T/2 - 1/2)}}}
2nd time around: Ate {{{1/2}}} of REMAINING tarts, plus {{{1/2}}} more gives us a remainder of: {{{matrix(1,5, (1/2) * (T/2 - 1/2) - 1/2, "=",  T/4 - 1/4 - 1/2, "=", T/4 - 3/4)}}}
3rd time around: Ate {{{1/2}}} of REMAINING tarts, plus {{{1/2}}} more gives us a remainder of: {{{matrix(1,5, (1/2) * (T/4 - 3/4) - 1/2, "=",  T/8 - 3/8 - 1/2, "=", T/8 - 7/8)}}}
After 3rd time around, 1 tart remained. so we get: {{{matrix(1,3, T/8 - 7/8, "=", 1)}}}
T - 7 = 8 ----- Multiplying by LCD, 8
Original number of tarts, or {{{highlight_green(matrix(1,5, T, "=", 8 + 7, "=", 15))}}}