DISINI 2003FermatSolution
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F or an arbitrary real number x, we dene [x℄ to be the greatest integer. less than or equal
F or eah real number , we dene b to be the greatest integer whih.. is less than or
Since opposite sides in a rectangle are equal we can label the sides as shown.. The first four triangular numbers 1, 3, 6, and 10 are illustrated in
So we only need to look at the number of ways of choosing four numbers so that their sum is a multiple of 3 (that is, we do not need to worry about looking at the order of the
Since there are three line segments that join 3 points, these configurations look like a triangle and these are not fully connected. There are 4 such configurations, which we can see
For the difference between the largest and smallest of these numbers to be as large as possible, we would like one of the numbers to be as small as possible (so equal to 1) and
The comparison of perimeter is not too difficult to see if we complete figure S as shown and compare lengths.. The perimeters of R and S
The Euclidean version of this well-known theorem states that if the inter- nal angle bisectors of two angles of a triangle are equal, then the triangle is isosceles (see the book
