Convergence of Math People

[redghostx]

Has anyone looked at the question from the Singapore Math Quiz?  I figure that if people can debate the merits of VIP points, they can surely solve such an innocent question.

 

 

[cambridge02138]

Here's my thought process for my solution ...

 

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scroll down

 

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From A's first statement, B knows that C's birth month is July or Aug.

 

After A's first statement, B knows the b-day .. which signals to A that C's b-day is 7/16, 8/15, or 8/17.

 

After A's second statement, we can deduce that C's b-day is 7/16, since the fact that A's knowledge of the month is sufficient for A to know C's b-day implies that C's b-day can't be 8/15 or 8/17.

 

So, by the process of elimination, C's birthday has to be 7/16.

Edited April 13, 2015 by cambridge02138

[Grynn]

Actually A's second statement is not even necessary for us to reach the solution. Once informed that B knows, we find out by rapid process of elimination which date satisfies both sets of conditions.

 

 

The statements could really be simplified as follows:

 

A: B does not know.

B: I do now.

 

 

Quite elegant indeed. I'm sure the Greeks or someone thought of this long, long ago.

[cambridge02138]

Actually A's second statement is not even necessary for us to reach the solution. Once informed that B knows, we find out by rapid process of elimination which date satisfies both sets of conditions.

 

 

The statements could really be simplified as follows:

 

A: B does not know.

B: I do now.

 

 

Quite elegant indeed. I'm sure the Greeks or someone thought of this long, long ago.

Actually, you do need A's second statement to arrive at the solution.

 

With only A's first statement and B's statement, we (the reader) can only eliminate the answers down to 7/16, 8/15 and 8/17.

 

We need A's second statement to eliminate 8/15 and 8/17.

[redghostx]

It is beautiful in its simplicity and you do need all 3 statements. (:

Ex astris, scientia.

[cambridge02138]

It is beautiful in its simplicity and you do need all 3 statements. (:

Ex astris, scientia.

Yes, you do need all three statements.  Thanks for sharing this question with us ... it brought back memories of all those math competition questions from many years ago.

 

The competition format I disliked the most was the relay format, where you have 5 team members, with each answering 1 question.  After the first team member gets his answer, he passes to the second team member the Q1 answer, which is an input to Q2.  In turn, Q2 answer is the input to Q3, etc.  Each team member has to work in isolation, receiving only a question and the previous team member's answer.  The only way to get the correct Q5 answer is if each team member get the correct answer to his/her question.

Edited April 13, 2015 by cambridge02138

[Grynn]

I thought my name was Bernard for a minute - sorry, you all are, of course, correct about needing all three statements. 

 

[diablo2112]

Above solutions are correct.  Just have to work through each possibility.  I got July 16 as an answer with a few minutes of deduction.  Now, here's the real issue, if double VIP starts on July 15, does that change the answer?