Several people are sitting around a round table playing a card game with a deck of 50 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?

Explanation: Let \(p\) be the number of people at the table. Martin is dealt the **first card** (card #1). Martin is also dealt the **last card** (card #50). Since Martin receives the first card, the cards dealt immediately before and after the last card (card #50) must be dealt to Martin. For Martin to receive card #50, it means that card #49 must be the one dealt to the person immediately before Martin, and card #1 was dealt to Martin. The people are dealt cards in cycles of \(p\). Card numbers dealt to Martin are of the form \(1 + k \cdot p\), where \(k\) is a non-negative integer. Card #50 must be a card dealt to Martin, so: \(50 = 1 + k \cdot p\). \(49 = k \cdot p\). This means that \(p\) must be a **factor of 49**. The factors of 49 are 1, 7, and 49. The only option in the list that is a factor of 49 is **7**.