# Google Placement Papers

**Google Placement Papers**

**1. Write a haiku describing possible methods for predicting search traffic seasonality.**

**MathWorld’s search engine**

**seemed slowed this May. Undergrads**

**prepping for finals.**

**Q 2.**

** 1**

**1 1**

**2 1**

**1 2 1 1**

**1 1 1 2 2 1**

**What’s the next line?**

**312211. This is the “look and say” sequence in which each term after the first describes the previous term: one 1 (11); two 1s (21); one 2 and one 1 (1211); one 1, one 2, and two 1’s (111221); and so on. See the look and say sequence entry on MathWorld for a complete write-up and the algebraic form of a fascinating related quantity known as Conway’s constant.**

**3. You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling around. What dost thou do?**

**A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.**

**B) Use the laptop as a digging device to tunnel to the next level.**

**C) Play MPoRPG until the battery dies along with your hopes.**

**D) Use the computer to map the nodes of the maze and discover an exit path.**

**E) Email your resume to Google, tell the lead gnome you quit and find yourself in whole different world [sic].**

**In general, make a state diagram . However, this method would not work in certain pathological cases such as, say, a fractal maze. For an example of this and commentary, see Ed Pegg’s column about state diagrams and mazes .**

**4. What’s broken with Unix?**

**Their reproductive capabilities.**

**How would you fix it?**

**5. On your first day at Google, you discover that your cubicle mate wrote the textbook you used as a primary resource in your first year of graduate school. Do you:**

**A) Fawn obsequiously and ask if you can have an autograph.**

**B) Sit perfectly still and use only soft keystrokes to avoid disturbing her concentration**

**C) Leave her daily offerings of granola and English toffee from the food bins.**

**D) Quote your favorite formula from the textbook and explain how it’s now your mantra.**

**E) Show her how example 17b could have been solved with 34 fewer lines of code.**

**6. Which of the following expresses Google’s over-arching philosophy?**

**A) “I’m feeling lucky”**

**B) “Don’t be evil”**

**C) “Oh, I already fixed that”**

**D) “You should never be more than 50 feet from food”**

**E) All of the above**

**7. How many different ways can you color an icosahedron with one of three colors on each face?**

**For an asymmetric 20-sided solid, there are possible 3-colorings . For a symmetric 20-sided object, the Polya enumeration theorem can be used to obtain the number of distinct colorings. Here is a concise Mathematica implementation:**

**What colors would you choose?**

**8. This space left intentionally blank. Please fill it with something that improves upon emptiness.**

**For nearly 10,000 images of mathematical functions, see The Wolfram Functions Site visualization gallery .**

**9. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knight’s move away?**

**This problem is discussed in J. Cserti’s 1999 arXiv preprint . It is also discussed in The Mathematica GuideBook for Symbolics, the forthcoming fourth volume in Michael Trott’s GuideBook series, the first two of which were published just last week by Springer-Verlag. The contents for all four GuideBooks, including the two not yet published, are available on the DVD distributed with the first two GuideBooks.**

**10. It’s 2PM on a sunny Sunday afternoon in the Bay Area. You’re minutes from the Pacific Ocean, redwood forest hiking trails and world class cultural attractions. What do you do?**

**11. In your opinion, what is the most beautiful math equation ever derived?**

**There are obviously many candidates. The following list gives ten of the authors’ favorites:**

**1. Archimedes’ recurrence formula : , , ,**

**2. Euler formula :**

**3. Euler-Mascheroni constant :**

**4. Riemann hypothesis: and implies**

**5. Gaussian integral :**

**6. Ramanujan’s prime product formula:**

**7. Zeta-regularized product :**

**8. Mandelbrot set recursion:**

**9. BBP formula :**

**10. Cauchy integral formula:**

**12. Which of the following is NOT an actual interest group formed by Google employees?**

**A. Women’s basketball B. Buffy fans C. Cricketeers D. Nobel winners E. Wine club**

**13. What will be the next great improvement in search technology?**

**14. What is the optimal size of a project team, above which additional members do not contribute productivity equivalent to the percentage increase in the staff size?**

**A) 1 B) 3 C) 5 D) 11 E) 24**

**15. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)**

**This is the isoperimetric point , which is at the center of the larger Soddy circle. It is related to Apollonius’ problem . The three tangent circles are easy to construct: The circle around has diameter , which gives the other two circles. A summary of compass and straightedge constructions for the outer Soddy circle can be found in ” Apollonius’ Problem: A Study of Solutions and Their Connections” by David Gisch and Jason M. Ribando.**

**16. **

**{**

**long l=1024;**

**int i=1;**

**while(l>=1)**

**{ l=l/2;**

**i=i+1;**

**}**

**}**

**a)8 b)11 c)10 d)100 ans:b**

**17. This question is based on the complexity …**

**Q3) s->AB**

**A->a**

**B->bbA**

**Which one is false for above grammar.**

**18. Some Tree were given & the question is to fine preorder traversal.**

**19. One c++ program,to find output of the program..**

**20. If the mean failure hour is 10,000 and 20 is the mean repair hour. If the printer is used by 100 customer, then find the availability.**

**1)80% 2)90% 3)98% 4)99.8% 5)100%**

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