युरेकाचे आउट-ऑफ-द-बॉक्स विचार आव्हान 1

The out-of-the-box thinking in math is important because it enhances problem-solving abilities, develops analytical and logical reasoning skills, promotes clarity of thought and communication, and fosters critical thinking skills.Out of box thinking skills have broad applications and are valuable in many academic, professional, and everyday life situations.

## The Out-of-Box Thinking Challenge1

**A car has 4 tyres and 1 spare tyre. Each tyre can travel a maximum distance of 20000 kms before wearing off. What is the maximum distance the car can travel before you are forced to buy a new tyre? You are allowed to change tyres an unlimited number of times. **

एका कारमध्ये 4 टायर आणि 1 स्पेअर टायर आहेत. प्रत्येक टायर जास्तीत जास्त 20000 किलोमीटरचा प्रवास करू शकतो. तुम्हाला नवीन टायर घेण्यास भाग पाडण्यापूर्वी कार जास्तीत जास्त किती अंतर पार करू शकते? तुम्हाला अमर्यादित वेळा टायर बदलण्याची परवानगी आहे.

## Importance of out of Box Thinking

**Problem-solving:**Mathematical thinking enables individuals to approach and solve complex problems. It involves breaking down problems into smaller, more manageable parts, identifying patterns and relationships, and using logical reasoning to arrive at solutions.**Analytical skills:**Mathematical thinking develops analytical skills, which are crucial for interpreting and analyzing data.**Logical reasoning:**Mathematics is based on rigorous logic and reasoning. Thinking in math helps individuals develop logical thinking skills, which involve making deductions, evaluating arguments, and drawing logical conclusions based on given information. These skills are applicable not only in mathematics but also in decision-making processes in various fields, including law, philosophy, and computer programming.**Precision and clarity**: Mathematics requires precise and clear thinking. It helps individuals develop the ability to articulate their thoughts and ideas precisely, using appropriate mathematical language and symbols. This clarity of thought is valuable not only in mathematical communication but also in written and verbal communication in general.**Critical thinking**: Mathematical thinking fosters critical thinking, which involves questioning assumptions, evaluating evidence, and considering alternative perspectives. It encourages individuals to think deeply and critically about problems, solutions, and mathematical concepts.

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## Answer

Let four tyres be named 1, 2, 3 and 4 and the spare tyre be 5

- After the first 5000 kms replace 1 with 5.

Remaining distances (1,2,3,4,5) =(15000, 15000, 15000, 15000, 20000)

- After the first 10000 kms Put 1 back to its original position and replace 2 with 5. Remaining distances

Remaining distances (1,2,3,4,5) =(15000, 10000, 10000, 10000, 15000)

- After the first 15000 kms Put 2 back to its original position and replace 3 with 5. Remaining distances

Remaining distances (1,2,3,4,5) =(10000, 10000, 5000, 5000, 10000)

- After the first 20000 kms Put 3 back to its original position and replace 4 with 5. Remaining distances

Remaining distances (1,2,3,4,5) =(5000, 5000, 5000, 0, 5000)

** So the max distance a car can travel = 25000 kms**