# All Puzzles

• Let it be simple and as direct as possible.

Interviewer : Tell me how much time (in days) and money would you require to clean all the glasses of each and every building (which is obviously composed of glasses) of New York City including all the glasses at the top as well as at the bottom of all buildings. Also mention the calculations for your contract and the money you would mostly prefer to accomplish this task. Most importantly you and only you have to do this job (i.e. you can’t ask anyone else to clean the glasses for you). You can even separately mention the costing of cleaning the window glasses and fixed glasses from both the sides (i.e. from inside as well as outside.)

* Time allotted for the question (to think and analyse) is half-an-hour.
** This was the most tricky, diplomatic and mind-manipulating question asked at one of the interviews conducted by Google for a highly paid job.

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• This was the second problem for Google Code Jam Qualification round 2014, if you are able to solve this problem with the first one(which is very easy) you will be eligible for the next round.

### Problem

Once you have X cookies that you haven’t spent on farms, you win! Figure out how long it will take you to win if you use the best possible strategy.

### Example

Suppose C=500.0, F=4.0 and X=2000.0. Here’s how the best possible strategy plays out:

1. After 250 seconds, you will have C=500 cookies and can buy a farm that producesF=4 cookies per second.

1. After buying the farm, you have 0 cookies, and your total cookie production is 6 cookies per second.

1. The next farm will cost 500 cookies, which you can buy after about 83.3333333seconds.

1. After buying your second farm, you have 0 cookies, and your total cookie production is 10 cookies per second.

1. Another farm will cost 500 cookies, which you can buy after 50 seconds.

1. After buying your third farm, you have 0 cookies, and your total cookie production is 14 cookies per second.

1. Another farm would cost 500 cookies, but it actually makes sense not to buy it: instead you can just wait until you have X=2000 cookies, which takes about142.8571429 seconds.

Total time: 250 + 83.3333333 + 50 + 142.8571429 = 526.1904762 seconds.

Notice that you get cookies continuously: so 0.1 seconds after the game starts you’ll have 0.2 cookies, and π seconds after the game starts you’ll have 2π cookies.

### Input

The first line of the input gives the number of test cases, TT lines follow. Each line contains three space-separated real-valued numbers: CF and X, whose meanings are described earlier in the problem statement.

CF and X will each consist of at least 1 digit followed by 1 decimal point followed by from 1 to 5 digits. There will be no leading zeroes.

### Output

For each test case, output one line containing “Case #x: y”, where x is the test case number (starting from 1) and y is the minimum number of seconds it takes before you can have X delicious cookies.

We recommend outputting y to 7 decimal places, but it is not required. y will be considered correct if it is close enough to the correct number: within an absolute or relative error of 10-6. See the FAQ for an explanation of what that means, and what formats of real numbers we accept.

### Limits

1 ≤ T ≤ 100.

#### Small dataset

1 ≤ C ≤ 500.
1 ≤ F ≤ 4.
1 ≤ X ≤ 2000.

#### Large dataset

1 ≤ C ≤ 10000.
1 ≤ F ≤ 100.
1 ≤ X ≤ 100000.

### Sample

 Input Output ```4 30.0 1.0 2.0 30.0 2.0 100.0 30.50000 3.14159 1999.19990 500.0 4.0 2000.0``` ```Case #1: 1.0000000 Case #2: 39.1666667 Case #3: 63.9680013 Case #4: 526.1904762```

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Albert Scholar
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• There was trouble from the Grundi. One of them
damaged the spaceship by hurling a rock at it. The
astronauts couldn’t figure out what the Grundi had to
gain by their hostile act. Was it just vandalism, done out
of sheer spite? Or perhaps not everyone on Mars was
happy to see the Earthlings return.
The Martian police chief brought in five Grundi for
questioning. Like all Grundi, they sometimes told the
truth and sometimes lied. The suspects each made
three statements, two of which were true and one of
which was false. And the guilty one was revealed.
1. Zum said:
I am innocent.
I have never used a rock to destroy anything.
Tset did it.
2. Uk said:
I did not do the damage.
The Earthman’s vehicle is on Grundi space.
Yan is not my friend.
3. Pala said:
I am innocent.
I never saw Yan before.
Tset is guilty.
4. Tset said:
I did not throw the rock.
Yan did it.
Zum did not tell the truth when he said I did it.
5. Yan said:
I am innocent.
Uk is guilty.
Pala and I are old friends.
Who was the culprit?

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ravi Expert
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• You have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), ec, until you only visit the 100th door.

What state are the doors in after the last pass? Which are open which are closed?

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Anand Guru
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• There is a building of 100 floors
-If an egg drops from the Nth floor or above it will break.
-If it’s dropped from any floor below, it will not break.
You’re given 2 eggs.
Find N

How many drops you need to make?
What strategy should you adopt to minimize the number egg drops it takes to find the solution?

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Anand Guru
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