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The Curious Cases of Sassy Suzy’s Sixteen Secret Suitors*
Sassy Suzy received valentines from sixteen secret suitors who wrote their phone numbers of the back of their prospective cards.
On the front of each card Suzy wrote a unique sequence number, indicating the order in which the card was received.
Suzy sorted the cards, arranging them in a stack with the card received first (the one with the smallest sequence number) on top and the one received last on the bottom of the stack.
Next, Suzy drew three lines on a piece of paper, creating six cells, which she labeled A through F.
Suzy placed the stack of cards on cell A.
Then she moved it, in as few moves as possible, to cell F as follows:
Suzy moved one card at a time from the top of a non-empty stack onto another, possibly empty stack in a different cell.
Suzy never placed a card with a larger sequence number on top of one with a smaller sequence number.
After each move, Suzy sent a text message to the phone number that was written on the back of the card she had just moved.
How many messages did Sassy Suzy send?
How many fewer messages could Suzy have sent if she had fifteen suitors instead of sixteen?
A
B
C
D
E
F
0
* Rehashes No 370 from Henry Ernest Dudeney’s 536 Curious Problems & Puzzles, edited by Martin Gardner.