500 men are arranged in an array of 10 rows and 50 columns according to their heights. Tallest among each row of all are asked to come out. And the shortest among them is A. Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B. Now
who is taller A or B ?
Sunday, February 28, 2010
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I guess the answer is undetermined.
ReplyDeleteIt is true in the example you have given.
For example take 3*3 matrix (it can be extendable to (10*50)).
For this arrangement :
10 4 5
4 5 1
3 2 6
Now A is second person in the second row.
B is first person in third row.
A and B are different. Here A is taller than B.
But the other way , A shorter than B cannot happen. Let A is at position (i,j) in the matrix , which implies every other person in the i'th row has height less than A. During selecting the shortest person column wise, in every column that person gets selected who has height less than or equal to person at i'th row in that column.
Please correct me if I am wrong.
The way you have it set up you are correct. But you set it up wrong. The questions says you have to order the matrix from tallest to shortest. In your case it would be
ReplyDelete10|6|5
5|4|4
3|2|1
tallest in each row is
10
5
3
the shortest of these becomes A.
A = 3;
The shortest of each column is
3
2
1
the tallest of these becomes B.
B = 3;
500 men are arranged in an array of 10 rows and 50 columns according to their heights. Tallest among each row of all are asked to come out. And the shortest among them is A. Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B. Now
ReplyDeletewho is taller A or B ?
This is an ambiguous question, why? I'll show you.
"500 men are arranged in an array of 10 rows and 50 columns ACCORDING TO THEIR HEIGHTS."
It states that the men have been ordered by HEIGHT, but it doesn't state the guidelines on how they were ordered using their heights.
Example 1: Which means they could have been ordered from tallest to shortest with the first man starting in row 1 column 1 and the second in row 1 column 2. If they were ordered in that fashion then the person in row 10 column 1(AKA: person #451) would be A/B.
Example 2: If they were placed in the same fashion listed above, but ordered from shortest to tallest then the person in row 1 column 50(AKA: person #50) would be A/B.
The ambiguous interpretations above come to the same answer: Neither person A or B is taller because A/B is the same person.
Although those are just two of the ambiguous interpretations, however, most people will argue that the first interpretation is the implied interpretation, but the fact is that the answer is still ambiguous and perhaps indeterminable. why is it indeterminable? Because of the questions ambiguity.
Example 3: I could assume they were ordered in such a way that the tallest person goes into row 1 column 1 and the shortest person goes into row 1 column 2 and the second tallest person goes into row 1 column 3 and the second shortest person goes into row 1 column 4, etc...
It would look like this on a 3x3 grid:
1 9 2
8 3 7
4 6 5
Tallest among each row: 9, 8, 6; Shortest among them: 6
Shortest among each column: 1, 3, 2;
Tallest among them: 3
You see, that arrangement would in fact support this statement, "ACCORDING TO THEIR HEIGHTS" Why? Because they were arranged according to their heights, just not in order of their height. It's that simple.
Some people would still feel the need to argue that it's implied to order them from tallest to shortest but in reality this question is ambiguous which in turn makes it indeterminable.
When a question is ambiguous it creates a collision of interpretations with each person clinging onto their own interpretation or interpretations(see examples 1/2). With such beliefs people will start to argue their point of view until a solution is settled upon or they get irritated to the point of avoiding the situation all together, hence, the question is indeterminable or falsely determined.
This is one of the many reasons people need to understand semantics: TO GET THEIR POINT ACROSS CLEARLY!
Both will be same person.
ReplyDeleteBoth are same, what ever way you define the order in row or column
ReplyDeletewell as there is no description about arrangement of height..
ReplyDeleteone case like this is also possible.
9 8 7
10 2 1
8 5 3
now