3

Part of 2023 LMT Fall

Problems(2)

2023 Fall LMT Team #3 pickles and a fair coin

Source:

Adamand Topher are playing a game in which each of them starts with

2

pickles. Each turn, they flip a fair coin: if it lands heads, Topher takes

1

pickle from Adam; if it lands tails, Adam takes

2

pickles from Topher. (If Topher has only

1

pickle left, Adam will just take it.) What’s the probability that Topher will have all

4

pickles before Adam does?

2023 Fall Speed p3

Source:

Sam Wang decides to evaluate an expression of the form

x +2 \cdot 2+ y

. However, he unfortunately reads each ’plus’ as a ’times’ and reads each ’times’ as a ’plus’. Surprisingly, he still gets the problem correct. Find

x + y

.
Proposed by Edwin Zhao
Solution.

\boxed{4}

x+2*2+y=x \cdot 2+2 \cdot y

. When simplifying, we have

x+y+4=2x+2y

x+y=4

2023FAlLspeedalg