It has been a long time since i posted any math puzzles..here is one which i managed to solve yesterday,
"the nth statement in a list of 100 statements is "Exactly n of the statements in this list are false"
a) What conclusions can you draw from these statements?
b) Answer part (a) if the nth statement is "atleast n of the statements in this list are false"
c)Answer part (b) assuming that the list contains 99 statements.
For those of you who are finding it hard to understand the problem statement, here is an elaboration.
It simply means that there are 100 statements written down somewhere. Part (a) means that :-
1st line - "exactly 1 of the statements in this list are false"
2nd line- " exactly 2 of the statements in this list are false"
.
.
.
99th line- "exactly 99 of the statements in this list are false"
100th line- "exactly 100 of the statements in this list are false"
similarly for the other two parts..only the statement now changes..I ll give the answer tonight..till then the readers can try to think over!! all the best
"the nth statement in a list of 100 statements is "Exactly n of the statements in this list are false"
a) What conclusions can you draw from these statements?
b) Answer part (a) if the nth statement is "atleast n of the statements in this list are false"
c)Answer part (b) assuming that the list contains 99 statements.
For those of you who are finding it hard to understand the problem statement, here is an elaboration.
It simply means that there are 100 statements written down somewhere. Part (a) means that :-
1st line - "exactly 1 of the statements in this list are false"
2nd line- " exactly 2 of the statements in this list are false"
.
.
.
99th line- "exactly 99 of the statements in this list are false"
100th line- "exactly 100 of the statements in this list are false"
similarly for the other two parts..only the statement now changes..I ll give the answer tonight..till then the readers can try to think over!! all the best
2 comments:
The solution to that makes sense when you ASSUME that all the statements are written like that. There is nothing in the problem that states to assume that. That is not math. There are an numerous other statements that could have been used based on the details given.
What will you do when asked the same question but it means all the statements are different? Your answer would then be wrong. Coming from a text book, this is flawed teaching.
I know how it is really solved now, and it is not the same way you came to the correct solution:
Suppose the list has f false statements and (100 - f) true
statements. The only statement in the list which truly describes this situation is
"Exactly f of the statements in this list are false."
That's just one true statement, so 100 - f = 1.
--And they don't all have to be the same statement. That is what the 99th statement says, and it doesn't matter what the rest say -they are all false.
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