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Online Puzzle Series

Puzzle 2 results have been released. To see the results, click here.



Techfest 2009 is proud to announce the Online Puzzles Series. It will consist of 4 online puzzle question sets with questions varing from cryptology to probability to logic.


Important Dates

PUZZLEReleaseDeadlineResults
130th September 200814th October 200820th October 2008
230th October 200814th November 200820th November 2008
330th November 200814th December 200820th December 2008
430th December 200814th January 200920th January 2009

Information

  1. An entry can have only one member.
  2. In case of tie, preference will be given to the entry which has been submitted earlier.
  3. Grand prize to be given to the cumulative winner of the series.
  4. Also cool prizes will be given to the winner of individual quizzes.
  5. Send all your answers to onlinepuzzleseries@techfest.org having the subject 'Puzzle set<number> Answers'.

Puzzle 2 results have been released. Click here to see Puzzle 2 results.


For further queries contact:


Edul M Patel

Manager, Online Events
Techfest 2009
+91 99672 15225
edulpatel[at]techfest[dot]org


Puzzle 2 - Solutions

Winners

  1. Devesh Jhalani
  2. Shrey Singhal
  3. Nikhil Vij

Answers and Explanation

  1. Answer: 99
    You can save about 50% by having everyone guess randomly.
    You can save 50% or more if every even person agrees to call out the color of the hat in front of them. That way the person in front knows what color their hat is, and if the person behind also has the same colored hat then both will survive.
    So how can 99 people be saved? The first wise man counts all the red hats he can see (Q) and then answers "blue" if the number is odd or "red" if the number is even. Each subsequent wise man keeps track of the number of red hats known to have been saved from behind (X), and counts the number of red hats in front (Y).
    If Q was even, and if both X and Y are either even or odd, then the wise man would answer blue. Otherwise the wise man would answer red.
    If Q was odd, and if both X and Y are either even or odd, then the wise man would answer red. Otherwise the wise man would answer blue.
    There can be any number of red hats, as the following examples show:


    Another example might also help, as this puzzle seems to trip up most people.


  2. Pick out two cards of the same suit. Select a card for Alex where adding a number no greater than six will result in the number of the other card of the same suit. Adding one to the Ace would cycle to the beginning again and result in a Two. For example, if you have a King and a Six of Diamonds, hand the King to Alex. The other three cards will be used to encode a number from 1 through 6. Devise a system with Peter to rank all cards uniquely from 1 to 52 (e.g. the two of hearts is 1, the two of diamonds is fourteen etc.). That will allow you to choose from six combinations, depending on where you put the lowest and highest cards.

  3. The team nominates a leader. The group agrees upon the following rules:
    The leader is the only person who will announce that everyone has visited the switch room. All the prisoners (except for the leader) will flip the first switch up at their very first opportunity, and again on the second opportunity. If the first switch is already up, or they have already flipped the first switch up two times, they will then flip the second switch. Only the leader may flip the first switch down, if the first switch is already down, then the leader will flip the second switch. The leader remembers how many times he has flipped the first switch down. Once the leader has flipped the first switch down 44 times, he announces that all have visited the room.
    It does not matter how many times a prisoner has visited the room, in which order the prisoners were sent or even if the first switch was initially up. Once the leader has flipped the switch down 44 times then the leader knows everyone has visited the room. If the switch was initially down, then all 22 prisoners will flip the switch up twice. If the switch was initially up, then there will be one prisoner who only flips the switch up once and the rest will flip it up twice.
    The prisoners can not be certain that all have visited the room after the leader flips the switch down 23 times, as the first 12 prisoners plus the leader might be taken to the room 24 times before anyone else is allowed into the room. Because the initial state of the switch might be up, the prisoners must flip the first switch up twice. If they decide to flip it up only once, the leader will not know if he should count to 22 or 23.
    In the example of three prisoners, the leader must flip the first switch down three times to be sure all prisoners have visited the room, twice for the two other prisoners and once more in case the switch was initially up.

  4. Answer: B=7, R=6, A=4, I=5 and N=9
    Make total 10 equations, 5 for rows and 5 for columns, and solve them.
    From Row 3 and Row 4,
    N + I + A + B + B = N + I + B + A + I + 2
    B = I + 2

    From Row 1 and Row 3,
    B + R + A + I + N = N + I + A + B + B - 1
    R = B - 1

    From Column 2,
    R + B + I + I + R = 29
    B + 2R + 2I = 29
    B + 2(B - 1) + 2I = 29
    3B + 2I = 31
    3(I + 2) + 2I = 31
    5I = 25
    I = 5

    Hence, B=7 and R=6
    From Row 2,
    B + B + R + B + A = 31
    3B + R + A = 31
    3(7) + 6 + A = 31
    A = 4

    From Row 1,
    B + R + A + I + N = 31
    7 + 6 + 4 + 5 + N = 31
    N = 9

    Thus, B=7, R=6, A=4, I=5 and N=9

  5. Statement (4) is false. There are 3 men, 8 women and 6 children.
    Assume that Statements (4), (5) and (6) are all true. Then, Statement (1) is false. But then Statement (2) and (3) both cannot be true. Thus, contradictory to the fact that exactly one statement is false.
    So Statement (4) or Statement (5) or Statement (6) is false. Also, Statements (1), (2) and (3) all are true.
    From (1) and (2), there are 11 men and women. Then from (3), there are 2 possible cases - either there are 8 men and 3 women or there are 3 men and 8 women.
    If there are 8 men and 3 women, then there is 1 child. Then Statements (4) and (5) both are false, which is not possible.
    Hence, there are 3 men, 8 women and 6 children. Statement (4) is false.

  6. Total possible combinations are 12869.
    It is given that you can order maximum of 8 items and you are allowed to have less than 8 items. Also, the order of purchase does not matter. Let's create a table for ordering total N items using X products.

    Thus, total possible combinations are:
    64 + 784 + 3136 + 4900 + 3136 + 784 + 64 + 1 = 12869

  7. The value of J must be 9.
    Since there are no leading zeros, J must be 7, 8, or 9. (JJJ = ABC + DEF + GHI = 14? + 25? + 36? = 7??)
    Now, the remainder left after dividing any number by 9 is the same as the remainder left after dividing the sum of the digits of that number by 9. Also, note that 0 + 1 + ... + 9 has a remainder of 0 after dividing by 9 and JJJ has a remainder of 0, 3, or 6.
    The number 9 is the only number from 7, 8 and 9 that leaves a remainder of 0, 3, or 6 if you remove it from the sum 0 + 1 + ... + 9. Hence, it follows that J must be 9.

  8. Cindy is the Singer. Mr. Clinton or Monika is the Dancer.
    From (1) and (3), the singer and the dancer, both cannot be a man. From (3) and (4), if the singer is a man, then the dancer must be a man. Hence, the singer must be a woman.

  9. The blindfolded man requires 5 turns.
    1. Open two adjacent holes.
    2. Open two diagonal holes. Now at least 3 holes are open. If 4th hole is also open, then you are done. If not, the 4th hole is close.
    3. Check two diagonal holes.
      • If one is close, open it and all the holes are open.
      • If both are close, open any one hole. Now, two holes are open and two are close. The diagonal holes are in the opposite status i.e. in both the diagonals, one hole is open and one is close.

  10. David is the guilty.
    Note that "All four of them hoped that something would occur that would facilitate his escape". It makes Clement's statement B True and David's statement B False.
    Now consider each of them as a guilty, one at a time.

    Since in total, three statements are true and five statements are false. It is clear from the above table that David is?

View the Puzzle 2 »


Puzzle 2

Rules:

  1. The Second set contains Ten questions. You are at liberty to use any tools you like to crack the questions, except bribing the quizmasters.
  2. Unless otherwise stated, please give full fundae/full connect to all questions and parts thereof. Any answer(s) not adhering to this rule is/are in danger of being marked as half correct.
  3. Please do not question the quizmasters marking scheme. All decisions regarding the entries may be thought of as full and final.
  4. Send your answers to onlinepuzzleseries[at]techfest[dot]org, latest by midnight of 14th November 2008. The first person to crack all the questions or to crack the maximum number of questions wins.

  1. The Stark Raving Mad King
    A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.
    The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.
    The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.
    The king will then move on to the next wise man and repeat the question.
    The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.
    What is the maximum number of men they can be guaranteed to save?

  2. I ask Alex to pick any 5 cards out of a deck with no Jokers.
    He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Peter can't see any of this). I look at the cards and I pick 1 card out and give it back to Alex. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Peter.
    Peter looks at the 4 cards i gave him, and says out loud which card Alex is holding (suit and number). How?
    The solution uses pure logic, not sleight of hand. All Peter needs to know is the order of the cards and what is on their face, nothing more.

  3. The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another".
    "In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything".
    "After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell".
    "No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead".
    "Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, We have all visited the switch room".
    "If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you."
    What is the strategy they come up with so that they can be free?

  4. Each of the five characters in the word BRAIN has a different value between 0 and 9. Using the given grid, can you find out the value of each character?

    B     R     A     I     N     31
    B     B     R     B     A     31
    N     I     A     B     B     32
    N     I     B     A     I     30
    I     R     A     A     A     23
    37   29   25   27   29

    The numbers on the extreme right represent the sum of the values represented by the characters in that row. Also, the numbers on the last raw represent the sum of the values represented by the characters in that column. e.g. B + R + A + I + N = 31 (from first row)

  5. At the Party:
    1. There were 9 men and children.
    2. There were 2 more women than children.
    3. The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible.

      Also, of the three groups - men, women and children - at the party:
    4. There were 4 of one group.
    5. There were 6 of one group.
    6. There were 8 of one group.

    Exactly one of the above 6 statements is false.
    Can you tell which one is false? Also, how many men, women and children are there at the party?

  6. McDonald's has just launched a new advertising campaign. The poster shows 8 McDonald's products and underneath claims there are 40312 combinations of the above items.
    Given that the maximum number of items allowed is 8, and you are allowed to have less than 8 items, and that the order of purchase does not matter (i.e. buying a burger and fries is the same as buying fries and a burger)
    How many possible combinations are there? Are McDonald's correct in claiming there are 40312 combinations?

  7. Consider the sum: ABC + DEF + GHI = JJJ.
    If different letters represent different digits, and there are no leading zeros, what does J represent?

    • One of the four people - Mr. Clinton, his wife Monika, their son Mandy and their daughter Cindy - is a singer and another is a dancer. Mr. Clinton is older than his wife and Mady is older than his sister.
    • If the singer and the dancer are the same sex, then the dancer is older than the singer.
      If neither the singer nor the dancer is the parent of the other, then the singer is older than the dancer.
    • If the singer is a man, then the singer and the dancer are the same age.
    • If the singer and the dancer are of opposite sex then the man is older than the woman.
    • If the dancer is a woman, then the dancer is older than the singer.

    Whose occupation do you know? And what is his/her occupation?

  9. A blindfolded man is asked to sit in the front of a carrom board. The holes of the board are shut with lids in random order, i.e. any number of all the four holes can be shut or open.
    Now the man is supposed to touch any two holes at a time and can do the following:
    • Open the closed hole.
    • Close the open hole.
    • Let the hole be as it is.

    After he has done it, the carrom board is rotated and again brought to some position. The man is again not aware of what are the holes which are open or closed.
    How many minimum number of turns does the blindfolded man require to either open all the holes or close all the holes?
    Note that whenever all the holes are either open or close, there will be an alarm so that the blindfolded man will know that he has won.

  10. When Socrates was imprisoned for being a disturbing influence, he was held in high esteem by his guards. All four of them hoped that something would occur that would facilitate his escape. One evening, the guard who was on duty intentionally left the cell door open so that Socrates could leave for distant parts.
    Socrates did not attempt to escape, as it was his philosophy that if you accept society's rules, you must also accept it's punishments. However, the open door was considered by the authorities to be a serious matter. It was not clear which guard was on that evening. The four guards make the following statements in their defense:

    Aaron:
    A) I did not leave the door open.
    B) Clement was the one who did it.

    Bob:
    A) I was not the one who was on duty that evening.
    B) Aaron was on duty.

    Clement:
    A) Bob was the one on duty that evening.
    B) I hoped Socrates would escape.

    David:
    A) I did not leave the door open.
    B) I was not surprised that Socrates did not attempt to escape.

    Considering that, in total, three statements are true, and five statements are false, which guard is guilty?