Brute Force in solving a Math Olympiad-type problem
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A Tough Geometry Problem
Question Triangle ABC has AC = BC, angle(ACB) = 96 degrees. D is a point in triangle…
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A Math Proportion Quiz Question
Question If a hen and a half can lay an egg and a half in a day and…
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Trigonometrical Proof Question
Question You have a triangle RST. Prove SinR^2 + CosR^2 = 1 given ST is perpendicular to RT….
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A Number Theory Problem: “How many numbers greater than 3000 can be formed from 1,2,3,4,5 without repeating any of them? How many will be even?”
Answer There are two type of numbers greater than 3000 that can be formed here namely, 4 digit…
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A Diophantine Equation: “How can I find all natural numbers a &b such that a^2 + a + 1 = b^2?”
Answer We assume “natural numbers here includes the number zero” (an old convention – may not be valid…
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Function: Range Problem
Question What is the range of the function f ( x ) = xsquared + 4 when the…
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In triangle ABC, angle ABC=15 degrees, angle ACB=30 degrees, AD is the median to side BC, A-D-C. angle BAD=?
Answer We will use the Sine Rule. In triangle ABD, AD / sin(ABD) = BD / sin(BAD) So…
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Calculate the square root of this number (without a calculator): 2000*2001*2002*2003+1
Answer The trick is to realize that the product of four consecutive integers is always less than 1…
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Add to make Perfect Squares
Question What must be added to each of the following expressions to obtain a perfect square? [Q1] a^2…