• Brain Teasers & Puzzles

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• How many tigers are there in the picture?

some say there are 4 tigers, some say 9, some say 20
can you find out how many tigers are there?

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ravi Expert
• 783.2K views

• The number of hours left today is half of the number of hours already passed. What time is it?
A. 8:00 a.m.
B. 12:00
C. 14:00
D. 16:00

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ravi Expert
• 781.1K views

• Here is snippet of section A of the curious multiple-choice entrance exam into the exclusive Puzzlefry puzzle club.

1. The first question with B as the correct answer is:

A. 1
B. 4
C. 3
D. 2

2. The answer to Question 4 is:

A. D
B. A
C. B
D. C

3. The answer to Question 1 is:

A. D
B. C
C. B
D. A

4. The number of questions which have D as the correct answer is:

A. 3
B. 2
C. 1
D. 0

5. The number of questions which have B as the correct answer is:
A. 0
B. 2
C. 3
D. 1

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ravi Expert
• 781.4K views

• After the recent Puzzle  annual marathon, the judges were comparing notes to determine who finished where. From their notes, can you help them to reconstruct the final result?

• Matthew Merryman beat Tom Trent and Jimmy James.
• Peter Piper beat Jimmy James, Tom Trent and Alan Ardman.
• Zach Zebra lost to Peter Piper.
• Graham Goodfellow beat Tom Trent
• Zach Zebra beat Frank Flintbone.
• Graham Goodfellow lost to Frank Flintbone and Peter Piper.
• Tom Trent beat Brian Brick.
• Alan Ardman beat Zach Zebra, Kevin Kingfisher and Graham Goodfellow.
• Kevin Kingfisher lost to Graham Goodfellow and Matthew Merryman.
• Brian Brick beat Kevin Kingfisher.
• Matthew Merryman lost to Alan Ardman and Zach Zebra.
• Frank Flintbone beat Tom Trent, Matthew Merryman and Brian Brick.
• Tom Trent lost to Jimmy James and Alan Ardman.
• Jimmy James beat Graham Goodfellow and Brian Brick.
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ravi Expert
• 780.8K views

• At the recent spring fete, four keen gardeners were displaying their fine roses.

In total there were four colours and each rose appeared in two colours.

From the clues below can you tell who had which colour roses?

• Mr Green had a yellow rose.
• Mr Yellow did not have a red one.
• Mr Red had a blue rose but not a green one.
• Mr Blue did not have a yellow one.
• One person with a red rose also had a green one.
• One person with a yellow rose also had a blue one.
• One of the persons with a green rose had no red.
• Neither of the persons with a yellow rose had a green one.
• No person has two roses of the same colour.
• No two persons had the same two colour roses and their names provide no clues.
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ravi Expert
• 781.0K views

• Puzzlefry bought 2 teapots,

If teapot A holds 32 cups of tea, about how many cups of tea does teapot B hold?

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• 789.2K views

• A king wants an advisor and comes to ask the 3 wisest sages.

He blindfolds them and put the hats on their head. Afterwards, the king takes off their blindfolds. He tells them that their hat is either blue or white. He tells them that whoever can deduce the color of their hat will be his next advisor. Also he tells them that at least one of the sages will be wearing a blue hat. The sages can all see each other’s hats except of course, their own. Sage A sees that the other 2 are wearing blue hats.
For hours no one spoke, then Sage A stands up and tells the  king the colour of his hat. What color is it and how does he know?

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Albert Scholar
• 783.4K views

• King Akbar asked Birbal

Write something on this wall, which if read in good times, makes you sad and if read in your bad time, makes you happy.

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Albert Scholar
• 783.1K views

• 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
• 781.1K views

• You are trying to cook an egg for exactly fifteen minutes, but instead of a timer, you are given two ropes which burn for exactly 1 hour each. The ropes, however, are of uneven densities – i e , half the rope length-wise might take only two minutes to burn. How can you cook the egg for exactly fifteen minutes?

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Albert Scholar
• 782.0K views

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