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Cookie Clicker Alpha Solution – Google Code Jam 2014

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This is 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

In this problem, you start with 0 cookies. You gain cookies at a rate of 2 cookies per second, by clicking on a giant cookie. Any time you have at least C cookies, you can buy a cookie farm. Every time you buy a cookie farm, it costs you C cookies and gives you an extra F cookies per second.

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.
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9 temples with 100 steps

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Number Puzzle #83

9 temples 100 steps puzzle

9 temples 100 steps puzzle

A person has some money in his pocket. He visits 9 temples on the way, every temple has 100 steps. he puts Rs.1 on each step while going up and as well as while coming back. On each temple he offers half of the money from his pocket to god, that way his pocket gets empty after 9th temple.
How many Rs. he had initially?

–In Hindi–
Ek aadmi kuch paise leke nikalta hai, raaste me 9 mandir hai ,har mandir me 100 sidiya hai, wo har mandir ki sidiyo pe jate waq 1 ..1..rupia rakhta hai, aate waqt bhi 1..1..rupia rakhta hai,…har mandir me jeeb me bache hove aadhe paise deta hai,….is tarah…jab wo akhri mandir se utarta …to us ke paas ke sab paise khatam ho jate hai,…..sawal ye hai .ke wo kitne paise leke nikalta hai…”


Check your answer:-

Tried enough already?
Click here to See Solution
Answer: he had a total of Rs.1,46,900 in his pocket initially.
How? We should start from last temple here.
he offered Rs.100 while coming back so he must have offered Rs.100 to the god on 9th temple and offered Rs.100 while going up on the 9th temple. so he had Rs.300 before 9th temple.

similarly before 8th temple: (300+100)*2 + 100 = 900
similarly before 7th temple: (900+100)*2 + 100 = 2100
similarly before 6th temple: (2100+100)*2 + 100 = 4500, we had some error here in calculating, thanks to our readers for correcting us
similarly before 5th temple: (4500+100)*2 + 100 = 9300
similarly before 4th temple: (9300+100)*2 + 100 = 18900
similarly before 3rd temple: (18900+100)*2 + 100 = 38,100
similarly before 2nd temple: (38100+100)*2 + 100 = 76500
similarly before 1st temple: (76500+100)*2 + 100 = 153300

Number Puzzle #68, 1, 10, 30, ?, 130

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Number Puzzle #68

missing number in 1, 10, 30, ??, 130

missing number in 1, 10, 30, ??, 130

Check your answer:-

Tried enough already?


Click here to See Solution

Actually this is a GP with first element as 1 and variable factor. where the factor comes from this series
1, 3, 7, 13.

Tn = Tn-1 + 2^(n-1);
T1 = 1;
T2 = T1 + 2^(2-1)= 1 + 2 = 3;
T3 = T2 + 2^(3-1) = 3 + 4 = 7;
T4 = T3 + 2^(4-1) = 7 + 6 = 13

nth number in GP = first number * (10)(Tn-1 in series);
First Element in GP = 1;
Second Element in GP(i.e. n = 2) = 1*10*(T1 in series); = 10
Third element in GP(i.e. n =3) = 1*10*(T2 in series) = 1*10*3 = 30
Fourth element in GP (i.e. n =4) = 1*10*(T3 in series) = 1*10*7 = 70
Fifth element in GP (i.e. n =5) = 1*10*(T4 in series) = 1*10*13 = 130

Thus the missing number here is 70.

How many toffee’s you can get in Rs.15

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Number Puzzle #65
Cost of one toffee is Rs.1 and as a special promotion scheme you get 1 toffee free for three wrappers.
How many toffee’s you can get in Rs.15?


–In Hindi– 1 rs ki ek toffee. 3 wrappers k sath ek aur toffee milti hai.. u’v got Rs.15.. how many total toffee’s u get?

Check your answer:-

Tried enough already?
Click here to See Answer
First of all you get 15 toffee in Rs.15, then you get 15/3 = 5 toffees from 15 wrappers.

Now you have 5 wrappers => 1 toffee + 2 wrappers => 3 wrappers => 1 toffee
Total number of toffees you get => 15 + 5 + 1 + 1 => 22 toffee’s.

X is impossible 4 GOD

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X is a 7 letter word,
X is impossible 4 GOD,
new babies like X better than milk,
the poor have X and the rich look for X from the poor,
if you eat X you will die,
X is more important than your life.
I swear with my life I will give you X if you get the answer.
What is X?

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Number puzzle from month name

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Here is a list showing the month and a number for each

January 73
February 83
March 51
April 52
May 31
June 42
July 41
August 63

Decipher the logic and find the number for September.

Click here to see Answers

Answer is 93.
How?
If you observe first number is the number of letters and the second number is the number of vowels present in the month spelling. Thus for september it should be 93.

4 bottles and water puzzle

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There are two bottles of 10 liter; each completely filled with water. Now 2 persons having empty bottles of 4 liter and 5 liter want to take 2-2 liters of water. You can use only these 4 bottles (10 liter-full, 10 liter-full, 5 liter-empty, 4 liter-empty) to transfer the water. Wasting or throwing of water is not permitted. How can this be done?

Note: It is assumed that you can not measure water level by comparing water level, or by judging, it should be exact 2 liters of water finally in each 4 and 5 liter water bottle.

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13 caves and a thief

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Find Minimum number of days to guarantee to catch the thief

13 caves and a thief puzzle

13 caves and a thief puzzle

There are 13 caves arranged in a circle. There is a thief hiding in one of the caves. Each day the the thief can move to any one of of the caves that is adjacent to the cave in which he was staying the previous day. And each day, you are allowed to enter any two caves of your choice.

What is the minimum number of days to guarantee in which you can catch the thief?

Note:

  1. Thief may or may not move to adjacent cave.
  2. You can check any two caves, not necessarily be adjacent.
  3. If thief and you exchange your caves, you will surely cross at some point, and you can catch the thief immediately.

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How many children, ladies and gents are there?

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One family of 20 members have 20 chapatis to eat, finally

  1. Every child gets 1/2 chapati
  2. Every Lady in the house gets 2 chapatis
  3. And every gentleman gets 3 chapatis to eat.

How many Child, Ladies and Gents are there in the family?

See Answers

There are two possible answers:
Answer1: Number of children = 14, Ladies= 5 and Gents = 1
Answer2: Number od children = 16, Ladies = 0 and Gents = 4.
How?
We can form the mathematical equations and solve them, lets assume number of children = x, ladies = y and gents = z.

Then we can form these two equations

  1. x + y + z = 20(Total number of people in family)
  2. x/2 + 2y + 3z = 20 (Total number of chapati’s)

Now we can solve above two equations as below

x/2 + 2(y+z) + z = 20
x/2 + 2(20 -x) + z = 20 (replaced y+z from first equation)
40 + z -3x/2 = 20
3x/2 = 20 +z
as z > 0 => 3x/2 > 20, x = 14, 16, 18...

We can see that y becomes negative for any value of x greater than or equal to 18,thus x = 14 and 16 are two possible values. we can get the corresponding values of y and z as well.

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