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2017 InIMC keystage2-EMIC individual Question 4

xIMC · 2017 InIMC keystage2-EMIC individual

Question 4

Each of $A$ and $B$, both starting with 50 dollars each, are taking turns in tossing a coin. If the coin lands heads, the other player losses 4 dollars and if the coin lands tails, the other player wins 3 dollars. After each player has tossed the coin 10 times, $A$ has 42 dollars more than $B$. If $A$ got heads 6 times, how many times did $B$ get heads?

**Source clarification.** The [organizer's Traditional Chinese edition](https://chiuchang.org/wp-content/uploads/sites/2/2018/01/2017InIMC_Keystage_II_Individual_TC.x17381.pdf), physical page 2, explicitly states: on heads, the opponent pays the tosser 4 dollars; on tails, the tosser pays the opponent 3 dollars. This transfer rule is omitted from the supplied English wording.