Leo and Chris are playing a game to settle who is the best among them. Each of them
can pick up either 2, 3, 4, or 5 oranges from a pile of oranges. They each play
alternatively and the person who is left to pick the last orange is the loser. Given that
there are 54 oranges and Leo plays first, how many oranges should Leo pick in his first
turn to guarantee his win?
Answers
Answer:
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Step-by-step explanation:
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Answer:
The number of oranges that Leo should pick at first to guarantee his win is 3
Step-by-step explanation:
Given: Leo and Chris can pick up either 2, 3, 4, or 5 oranges from a pile of oranges. here are 54 oranges and Leo plays first. Both play alternatively and the person who is left to pick the last orange is the loser.
To Find: how many oranges should Leo pick in his first turn to guarantee his win?
Solution:
In this question,
Total oranges = 54
Minimum to be picked = 2
Maximum to be picked = 5
The above Question can be used using a simple formula:
Number of Oranges to pick in first turn = Remainder of ((Total Oranges -
Minimum)/(Minimum+Maximum))
= Remainder of (( 54 - 2)/(2+5))
= Remainder of 52/7
= 3
Hence, the number of oranges that Leo should pick at first to guarantee his win is 3