http://nysmithmath.forumotion.net/higher-level-problems-f10/-t1.htm More difficult problems that are most likely above competition level mathematics. Sun, 29 Mar 2009 01:33:27 GMT 10 http://intranet.meriden.k12.ct.us/maloney/maloney_WEB/clubs/images/MathSymbols50_000.jpg http://nysmithmath.forumotion.net/higher-level-problems-f10/-t1.htm http://nysmithmath.forumotion.net/higher-level-problems-f10/a-little-problem-t63.htm theonlyMattinMathCounts
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 5 + 5
...

Two things:
1.) Was I lying before? Can every single one be expressed this way? How about 10234598692032 (or some really big number like that)?

2.) If every single one can be expressed this way, why?]]> Higher Level Problems Sun, 29 Mar 2009 01:33:27 GMT http://nysmithmath.forumotion.net/higher-level-problems-f10/a-little-problem-t63.htm#375 http://nysmithmath.forumotion.net/higher-level-problems-f10/a-little-problem-t63.htm http://nysmithmath.forumotion.net/higher-level-problems-f10/sizes-of-infinity-t57.htm theonlyMattinMathCounts Which of the following infinitely large sets is largest? a.) the set of all rational numbers b.) the set of all positive even numbers c.) the set of all positive odd numbers d.) the set of all real numbers from 0 to 1, inclusive e.) the set of all counting numbers (1, 2, 3, 4, ...) f.) All of the above sets are the same size. If your answer is a-e, provide a proof as to why the set you chose is larger. P.S. Where am I getting these points from? Here is the answer Spoiler:The ... Higher Level Problems Mon, 09 Mar 2009 01:45:35 GMT http://nysmithmath.forumotion.net/higher-level-problems-f10/sizes-of-infinity-t57.htm#332 http://nysmithmath.forumotion.net/higher-level-problems-f10/sizes-of-infinity-t57.htm http://nysmithmath.forumotion.net/higher-level-problems-f10/mega-sphere-t35.htm Steve A sphere 5.5 metres in diameter is filled with 1m diameter hemi-spheres. a(1) What is the theoretical maximum amount of hemi-spheres that can be crammed into the big sphere given that the following condition is met: Each hemi-sphere's flat side (which I'll now refer to as its 'disc') has a central point (indicated by the white point shown in the hemisphere diagram to the right). The point must not 'see' another hemisphere's disc. By definition, when I say 'see', the simplest thing to imagine ... Higher Level Problems Tue, 14 Oct 2008 15:18:37 GMT http://nysmithmath.forumotion.net/higher-level-problems-f10/mega-sphere-t35.htm#204 http://nysmithmath.forumotion.net/higher-level-problems-f10/mega-sphere-t35.htm http://nysmithmath.forumotion.net/higher-level-problems-f10/snooker-table-t27.htm Trevin Gandhi A 'snooker' table (measuring 8 metres by 4m) with 4 'pockets' (measuring 0.5m and placed at diagonal slants in all 4 corners) contains 10 balls (each with a diameter of 0.25m) placed at the following coords: 2m,1m...(white ball) ...and red balls... 1m,5m... 2m,5m... 3m,5m 1m,6m... 2m,6m... 3m,6m 1m,7m... 2m,7m... 3m,7m The white ball is then shot at a particular angle from 0 to 360 degrees (0 being north, and going clockwise). Just to make it clear, a ball is 'potted' if at ... Higher Level Problems Sun, 12 Oct 2008 21:13:59 GMT http://nysmithmath.forumotion.net/higher-level-problems-f10/snooker-table-t27.htm#131 http://nysmithmath.forumotion.net/higher-level-problems-f10/snooker-table-t27.htm