Puzzle:
| | I | II | III | IV | V |
| Chintan | c | b | True | True | False |
| Akash | c | c | True | True | True |
| Jignesh | a | c | False | True | True |
| Mukund | b | a | True | True | False |
| Venky | b | b | True | False | Tru |
Also, no two students got the same number of correct answers. Can you tell which are the correct answers? What are their individual score?
For Solution SCROLL DOWN...
Solution:
The correct answers are b, a, True, False and False. Also, the scores are Jignesh (0), Akash (1), Chintan (2), Venky (3) and Mukund (4).
As no two students got the same number of correct answers, the total number of correct answers must be either 15 (1+2+3+4+5) or 10 (0+1+2+3+4).
Let's find out the maximum number of correct answers possible from the answers given by them.
For Question I = 2 (b or c)
For Question II = 2 (b or c)
For Question III = 4 (True)
For Question IV = 4 (True)
For Question V = 3 (True)
Thus, the maximum number of correct answers possible are 15 (2+2+4+4+3) which means that Akash would have given all correct answers as only he answered True for questions III, IV and V. But then Chintan and Jignesh would have exactly 3 correct answers. And also, Mukund and Venky would have 2 correct answers. So no one got all five correct. One can also arrive at this conclusion by trial-and-error, but that would be bit lengthy.
Now, it is clear that total number of correct answers are 10 (0+1+2+3+4). Questions III and IV both can not be False. If so, total number of correct answers would not be 10. So the student who got all wrong can not be Chintan, Akash and Mukund.
If Venky got all wrong, then Chintan, Jignesh and Mukund each would have atleast 2 correct answers. It means that Akash would have to be the student with only one correct answer and the correct answers for questions I and II would be a and a respectively. But then the total number of correct answers would be 1 (a) + 1 (a) + 1 (False) + 4 (True) + 2 (Flase) = 9.
Thus, Jignesh is the student with all wrong answers. The correct answers are b, a, True, False and False. Also, the scores are Jignesh (0), Akash (1), Chintan (2), Venky (3) and Mukund (4).
44 comments:
1) b
2) a
3) true
4) false
5) false.
mukund--->4
venky --->3
chintan-->2
akash---->1
jignesh-->0
Sol
They got different scores
So their scores might be (1,2,3,4,5) or (0,1,2,3,4)
case 1) Assume that Chintan has answered all the 5 questions correctly
then aakash and mukund will get same score 3
So Chintan didnt get score 5
case 2)if Aakash gets score 5 Chintan and Jignesh will get same score 3
so on ........ (1,2,3,4,5) is not the answer.
for (0,1,2,3,4)
case 1)
Assume that answers are c,b,tr,tr,tr then chintan and aakash will get same score 4
so this is not the answer
case2) Assume answers are c,b,t,f,f
then aakash and mukund will get the same score 2. So this is not the answer
so on ......
Chintan didnt get the score 4
........
if mukund gets the score 4 and the answers are b,a,t,f,f, all members will get different scores
Let's assume someone answered all the Qs correctly.
The matrix below shows the score-chart ().
------------------C--A---J---M--V
C - c b T T F - 5 - 3 - 1 - 3 - 2
A - c c T T T - 3 - 5 - 3 - 2 - 2
J - a c F T T - 1 - 3 - 5 - 1 - 1
M - b a T T F - 3 - 2 - 1 - 5 - 2
V - b b T F T - 2 - 2 - 1 - 2 - 5
in each of the columns (or rows), at least one score appears more than once, so, none got all the answers right (i.e., nobody scored 5)
So someone must have got all the answers wrong (i.e., someone scored 0)
The answer combinations of the T-F Qs that have occurred are - FTT, TFT, TTF, TTT, one of which are all wrong answers, and the compliment of which r all correct.
so the possible correct cobinations are - TFF, FTF, FFT, FFF
if it was FFF, marks scored by the students for these 3 T-F Qs are
C - 1
A - 0
J - 1
M - 1
V - 1, but the highest scorer (who scores 4) has to score at least 2 in the last 3 Qs. So this is not a possible correct combination.
if it was TFF, marks scored by the students for these 3 T-F Qs are
C - 2
A - 1
J - 0
M - 2
V - 2
then, either cb(C highest scorer), ba(M highest scorer) or bb(V highest scorer) must be the possible correct answers for the first 2 Qs.
cb combination produces - 42023 (invalid)
ba combination produces - 21043 (which satisfies the criteria, and hence the answer)
So, the correct answers are baTFF
Couple answers posted here including the "official" one assume that if "no two students got the same number of correct answers." means the scores must be 1,2,3,4,5 or 0,1,2,3,4. But there are possibilities of havind combinations like 0,2,3,4,5; 0,1,3,4,5; etc. The fact that scores are 0,1,2,3,4 can be derived from the fact that no one got all answers right (which can be seen from the matrix posted above).
A little longer way, but to me it's more mathematically precise and explains a clear algorythm without guessing:
Step 1: As Sudip shows no one answered all questions correctly, so scores are 0,1,2,3,4.
Step 2. Let's define a function A(B) that returns the score for answering question A with answer B, A=I|II|III|IV|V and B=a|b|c|t|f. For example I(c) means the score for answering 'c' on the first question. Note that the function returns either 1 for correct answer or 0 for incorrect one.
Then the matrix can be rewritten as:
I(c)+II(b)+III(t)+IV(t)+V(t) = Sc (Chintan Score)
I(c)+II(c)+III(t)+IV(t)+V(t) = Sa
I(a)+II(c)+III(f)+IV(t)+V(t) = Sj
I(b)+II(a)+III(t)+IV(t)+V(f) = Sm
I(b)+II(b)+III(t)+IV(f)+V(t) = Sv
Sc!=Sa!=Sj!=Sm!=Sv => Sx-Sy!=0 for any x and y.
Sc-Sa=II(b)-II(c)+V(f)-V(t)!=0
Note that if II(b)=1 then II(c)=0 because only one of the answers for question II can be correct, similarly if V(f)=1 then V(t)=0. Considering these facts and the equasion the followinf can be derived:
if II(b)=1 then V(f)=1
if V(f)=1 then II(c)=0
if II(c)=1 then V(t)=1
if V(t)=1 then II(b)=0
Similarly from Sa-Sj we derive:
if I(c)=1 then III(t)=1
if III(t)=1 then I(a)=0
if I(a)=1 then III(f)=1
if III(f)=1 then I(c)=0
From Sc-Sm we derive:
if I(c)=1 then II(a)=0
if II(a)=1 then I(c)=0
if I(b)=1 then II(b)=0
if II(b)=1 then I(b)=0
From Sc-Sv we derive:
if IV(t)=V(t) (which means if answer to IV is the same as the answer to V) then I(c)!=I(b) => I(a)=0
From Sm-Sv we derive:
if IV(t)=V(t) then II(a)!=II(b) => II(c)=0
Step 3.
Let's inverse the original matrix. We know that one of the rows in the inversed matrix will be the correct answer (the one that is inversion of the answer that got 0 score). Using the rules derived in the Step 2 we ca eliminate some of the options. After that elimination the inverse matrix looks like:
C - a|b a|c f f t
A - b a|b f f f
J1- b a t f f
J2- c b t f f
M - a c f f t
V - a a f t f
Note that I split answers for J because in
J - b|c a|b t f f
b a t f f
b b t f f [not valid]
c a t f f [not valid]
c b t f f
The two options are not valid because of the rules derived from Sc-Sm.
Inverse matrix gives us 10 options:
C1 - a a f f t
C2 - a c f f t
C3 - b a f f t
C4 - b c f f t
A1 - b a f f f
A2 - b b f f f
J1 - b a t f f
J2 - c b t f f
M - a c f f t
V - a a f t f
Note that C2=M and therefore none of them can be the correct answer (otherwise both Chitan and Mukund would have 0 score). We narrowed down the options of the correct answer to 8. Good enough to just check which one of them is correct.
If C1 were correct answer Sa=Sm=1
If C3 were correct answer Sj=Sm=2
If C4 were correct answer Sj=Sv=3
If A1 were correct answer Sc=Sj=1
If A2 were correct answer Sc=Sm=2
J1 is correct answer Sc=2,Sa=1,Sj=0,Sm=4,Sv=3
Let's make sure it's the only one:
If J2 were correct answer Sa=Sm=2
If V were correct answer Sj=Sm=3
Therefore J1 (b a t f f) is the only correct answer.
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Playing bingo needs more than luck or skills and techniques, contrary to what most believe. Bingo, just like any game of chance, comes with rules and regulations that players should observe. Being a player comes with responsibilities and etiquette.
Winning the Game
The moment you figured out you won, you must immediately yell BINGO, and it should be loud enough for the floor walker to hear. The pot money shall be given to the winner once their winning card is confirmed. Well, in winning or once you know you just won, the most important thing is that you shout the winning word BEFORE the time elapses. If the game proceeds and the next number is mentioned and you failed to shout "Bingo", your winning card is disqualified. Therefore, this is the rule you must know.
There may be cases when there are two winners, and in this case the pot money shall be divided equally among the winners. Supposing there are two winning cards, the two winners will share half the prize money.
Bingo Game Rules
Bingo rules are basically the same no matter in which Online Bingo hall you play. But still it's good if you know these rules by heart. If it is your first try, then ask for handouts and inquire from pros regarding the game rules. Nonetheless, the ideal thing to do if you have questions is to ask the floor walker and not the person seated beside you. You should clarify things and doubts before the game starts because asking too many questions as the game proceeds could well distract you. This guideline also applies to those who are newcomers at casinos, those who play roulette for the first time.
Bingo halls demand an age limit of 18 years old. If you are below this age, you are prohibited to play. Some bingo houses ban alcohol inside, so players aren't supposed to take liquor nor drink it inside the venue. Smoking may also be restricted inside the venue, as there are designated smoking sections.
Take note that some Bingo houses don't allow food but some do, so it basically depends on the venue. Policies vary among different venues. For instance, some bingo halls allow reservation of cards, while others don't allow it. Some allow people to leave the venue in the middle of the game, others forbid it. But there are general policies observed in all bingo houses, such as disqualification of tampered bingo cards. There is no way you can get away with a tampered card because the walkers are adept at identifying authentic cards from tampered ones. You could be banned from a bingo establishment if proven liable of tampering a card. Hence, you should play honestly.
Interestingly, some venues offer special bingo games for kids although some halls don't allow players to have companions while playing. Suppose you bring kids with you, don't let them run around the venue and bother other gamers. They should behave well whilst you play and the game proceeds. Play quietly and don't recite the numbers you desperately want to come off because you'll be much of a disturbance if you do. Decorous playing is expectant of all players, even those who play roulette at casinos. Also, having a valid identification is important because you don't know you might win and need to present credentials.
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