Post by Countolaf on Jan 7, 2006 19:11:28 GMT 1
Some problems I found on a site:
Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Given that the above statements are true, what are the two numbers?
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Roll a standard pair of six-sided dice, and note the sum. There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:
1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
2. Each face has at least one dot.
3. The number of ways of obtaining each sum is the same as for the standard dice.
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Find all integer solutions of y² = x³ - 432
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Let x, y, n be positive integers, with n > 1. How many solutions are there to the equation x^n - y^n = 2100?
Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Given that the above statements are true, what are the two numbers?
------------------------------------------------------------------------
Roll a standard pair of six-sided dice, and note the sum. There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:
1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
2. Each face has at least one dot.
3. The number of ways of obtaining each sum is the same as for the standard dice.
-------------------------------------------------------------------------
Find all integer solutions of y² = x³ - 432
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Let x, y, n be positive integers, with n > 1. How many solutions are there to the equation x^n - y^n = 2100?
