Graph Theory and Combinatorics: 4. There are 13 squares of side 1 positioned ins

Question

Graph Theory and Combinatorics:

4. There are 13 squares of side 1 positioned inside a circle of radius 2. Show that at least 2 of the squares have a common point. 5. Show that S(5, 4) Is(5, 4). Can you see a combinatorial reason why this is true? 6. Explain why for a fixed n, the sum of the unsigned Stirling numbers of the first kind equals n! 7. For a permutation, a fixed point is an instance when i is in position i of the permutation. For example, the permutation 32541 has fixed points 2 and 4. Use inclusion-exclusion to count the number of permutations of 1, 2, . 8 with no fixed points.

Explanation / Answer

4) Given radius r = 2

then area of circle is r^2 = (2^2) = 4

= 12.56 < 13

Which is impossible.

On the other hand , if no 2 of the squares have a common point then total area is equals to the sum of their individual areas which is equal to 13.

So it is impossible for the squares to cover an area of 13.

Thus infact at least two of the squares shares a common point.

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.