Posted by help on Thursday, April 1, 2010 at 4:08pm.
According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is
their argument.
Given the obtuse angle x, we make a quadrilateral ABCD with DAB = x, and ABC =
90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to
AB at P. ThenPA = PB andPC = PD. So the trianglesPADandPBC have equal sides
and are congruent. Thus PAD = PBC. But PAB is isosceles, hence PAB = PBA.
Subtracting, gives x = PAD− PAB = PBC − PBA = 90◦. This is a preposterous
conclusion – just where is the mistake in the “proof” and why does the argument break down
there?
5. Consider a rectangular array of dots with an even number of rows and an even number of
columns. Color the dots, each one red or blue, in such a way so that in each row half the
dots are red and half are blue, and also in each column half are red and half are blue. Now,
whenever two points of the same color are adjacent (in a row or column), join them by an edge
of that color. Show that the number of red edges is the same as the number of blue edges.
6. The squares of an infinite chessboard are numbered as follows: in the first row and first column
we put 0, and then in every other square we put the smallest nonnegative integer that does not
appear anywhere below it in the same column or anywhere to the left of it in the same row.
What number will appear in the 1000th row and 700th column? Can you generalize?
7. Let’s agree to say that a positive integer is primelike if it is not divisible by 2, 3, or 5. How
many primelike positive integers are there less than 100? less than 1000? A positive integer
is very primelike if it is not divisible by any prime less than 15. How many very primelike
positive integers are there less than 90000? Without giving an exact answer, can you
say approximately how many very primelike positive integers are less than 1010? less than
10100? Explain your reasoning as carefully as you can.
8. Find a positive integer m such that
1
2m is a perfect square and
1
3m is a perfect cube. Can you
find a positive integer n for which
1
2n is a perfect square,
1
3n is a perfect cube and
1
5n is a
perfect fifth

math  PROMYS, Thursday, May 13, 2010 at 10:51pm
Now now..... no using outside sources!! If you continue to do this, we will track your IP address to find out who you are and disqualify you...

math  Anonymous, Friday, February 17, 2012 at 11:34am
Find a polynomial with integer coefficients for which √ √ is a root. That is find such that for some nonnegative integer , and integers
and(√ √) .

math  etovey, Sunday, February 23, 2014 at 10:30pm
promys uk tracking is not so easy especially not with a subponea

math  etovey, Thursday, March 13, 2014 at 10:03am
and it's illegal to buddy
Answer This Question
Related Questions
 Math  According to the Journal of Irreproducible Results, any obtuse angle is a...
 number theory  According to the Journal of Irreproducible Results, any obtuse ...
 maths  According to the Journal of Irreproducible Results, any obtuse angle is ...
 maths  According to the Journal of Irreproducible Results, any obtuse angle is ...
 maths  According to the Journal of Irreproducible Results, any obtuse angle is ...
 math  According to the Journal of Irreproducible Results, any obtuse angle is a...
 Geometry  Given: obtuse triangle ABC with obtuse angle B. Point D on side AC ...
 geometry  obtuse triangle ABC with obtuse angle B. Point D on side AC such that...
 math  how do you name a obtuse angle when you are naming an angle just look for...
 Geometry  Write an indirect proof that an obtuse triangle does not have a right...
More Related Questions