Solving A Classic Google Interview Logic Puzzle
TLDRThe video script presents a mathematical puzzle involving identifying the top three horses from a group of 25, given that only five can race at a time and no watches are available to measure exact times. The puzzle is often used in technical interviews at companies like Google. The solution involves a strategic approach with a minimum of seven races. First, the horses are divided into five groups and raced, followed by a race among the winners to determine the fastest horse. To find the second and third fastest, horses from the first, second, and third places of the winning group, and the first and second places of the second-place group, along with the fastest horse from the third-place group, are raced. This process eliminates horses slower than at least three others, narrowing down to the top three. The video explains the logic behind each step, ensuring viewers understand why the procedure is both sufficient and minimal, requiring exactly seven races.
Takeaways
- 🏇 The problem involves identifying the fastest three out of 25 horses with a limitation of racing up to five horses at a time.
- 🔢 The minimum number of races required to identify the top three horses is seven, as explained through a strategic process.
- 🤔 The first step is to race the horses in groups of five, which results in five initial races to determine the fastest horse from each group.
- 🏆 A sixth race involves the winners of the initial five races to find the absolute fastest horse.
- ✍️ Notation is introduced to label the groups and the order of finish within each group, e.g., A2 for the second-fastest horse in group A.
- 🐎 In the seventh and final race, horses that have the potential to be the second or third fastest are selected based on their performance in previous races.
- 🚫 Horses that are slower than at least three other horses are eliminated from contention for the top three spots.
- 🛑 Group E is entirely eliminated as all horses are slower than the winners of groups A, B, and C.
- 🔑 By process of elimination, only the top two horses from group B and the top horse from group C, along with the second and third from group A, are considered in the final race.
- ⏳ The final race determines the second and third fastest horses, as the winner is the second fastest and the runner-up is the third fastest.
- 📝 The procedure is deemed optimal because it is both sufficient and minimal, requiring exactly seven races to find the three fastest horses.
- 📈 The presenter, Presh Talwalkar, uses this puzzle to demonstrate strategic thinking and problem-solving, a common question in technical interviews.
Q & A
What is the minimum number of races needed to identify the fastest three horses among 25?
-The minimum number of races needed is seven.
Why can't we identify the fastest three horses with fewer than seven races?
-Because we need to race each of the 25 horses at least once, and since we can only race five at a time, we start with five races. Then, we need one more race to compare the winners, and at least one additional race to determine the second and third fastest horses among the remaining contenders.
How many horses are in each group during the initial races?
-Each group consists of five horses during the initial races.
What is the purpose of racing the winners of each initial group?
-The purpose is to identify the fastest horse overall, which is the winner of the winners' race.
How are the horses from the initial groups labeled for the final race to determine the second and third fastest horses?
-The horses are labeled with the group letter (A, B, C, D, E) and a subscript to denote their finishing order within that group (e.g., A2 for the second-fastest horse in Group A).
Why are all horses in Group E eliminated from being the second or third fastest?
-Because the fastest horse in Group E is slower than the winners of Groups A, B, and C, and thus all horses in Group E are slower than at least three other horses, they cannot be the second or third fastest overall.
Which horses are raced in the final race to determine the second and third fastest horses?
-The final race includes A2 (second-fastest in Group A), A3 (third-fastest in Group A), B1 (fastest in Group B), B2 (second-fastest in Group B), and C1 (fastest in Group C).
Why is the horse A1 not included in the final race?
-A1 is the fastest horse overall and has already been identified, so racing it again would not provide any new information.
What is the strategy for eliminating horses that cannot be the second or third fastest?
-The strategy is to eliminate any horse that is slower than at least three other horses, as it cannot be the second or third fastest if it's behind three others.
How does the process of elimination work in identifying the second and third fastest horses?
-By comparing the horses' performances against the winners and using the process of elimination, horses that are slower than three other horses are removed from contention. This narrows down the candidates to the six horses that could potentially be the second or third fastest.
What is the significance of the order in which the horses finished within their initial groups?
-The order is significant because it determines which horses from each group are contenders for the second and third fastest positions in the overall ranking.
Why is this problem sometimes asked as a technical interview question at companies like Google?
-The problem tests the candidate's ability to think critically, solve complex problems, and apply logical reasoning, which are valuable skills in a technical role.
Outlines
🏇 Identifying the Fastest Three Horses in 7 Races
In this paragraph, Presh Talwalkar presents a puzzle about identifying the fastest three horses out of 25, given that only five horses can race at a time. The puzzle is a common interview question for companies like Google. To solve it, one must conduct a series of races strategically. The solution involves initially racing the horses in groups of five, determining the fastest horse by racing the winners of these groups, and finally conducting a seventh race with specific horses to find the second and third fastest horses. This process is explained in detail, with the conclusion that seven races are both sufficient and the minimum required to solve the puzzle.
📉 Process of Elimination to Find the Second and Third Fastest Horses
This paragraph delves into the process of elimination to identify the second and third fastest horses after the fastest horse has been determined. It explains that horses slower than at least three others can be eliminated from contention. By systematically eliminating horses from groups E, D, and C, and then further refining the selection from groups B and A, the field is narrowed down to six horses. After removing the already identified fastest horse, a final race with the remaining five horses determines the second and third fastest horses. The paragraph concludes by affirming the minimal number of races required, providing reasoning for why seven races are both necessary and optimal for solving the puzzle.
Mindmap
Keywords
💡Horses
💡Races
💡Technical Interview Question
💡Puzzle Maker
💡Mechanical Horses
💡Printout
💡Groups
💡Winners Race
💡Process of Elimination
💡Optimal Procedure
💡Math and Game Theory
Highlights
The problem requires identifying the fastest three horses out of 25, with a maximum of five horses in a race and no watch to measure times.
The problem is a technical interview question sometimes asked by companies like Google.
25 mechanical horses complete the track in different pre-programmed times, and the goal is to find the top three without knowing their exact finishing times.
The minimum number of races needed to identify the fastest three horses is seven.
The procedure involves dividing the 25 horses into groups of five, racing them, and then using the winners to find the fastest horse.
After finding the fastest horse, a final race with specific horses from the previous races determines the second and third fastest horses.
The groups from the initial races are labeled A to E based on their finishing order in the race of winners.
Horses are labeled with a subscript to denote their finishing order within their respective groups.
The final race includes A2, A3, B1, B2, and C1 to determine the second and third fastest horses.
The procedure is detailed in a step-by-step explanation to ensure understanding of why it works.
The video illustrates the races and the arrangement of horses to visually convey the solution.
The fastest horse is determined by racing the winners of each initial group.
The process of elimination is used to identify the horses that could potentially be the second or third fastest.
Horses that are slower than at least three other horses are eliminated from contention.
The final race among the remaining horses identifies the second and third fastest horses.
The necessity of at least seven races is justified by the logical process of elimination and comparison.
The described procedure is proven to be optimal, providing a minimum number of races to solve the problem.
The video is educational, targeting an audience interested in math and game theory.
The presenter, Presh Talwalkar, invites viewers to subscribe to his channel and follow him on social media for more content on math and game theory.
Transcripts
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