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AD and AE are respectively the altitude and angle bisector of ΔABC (D and E are on side BC). If DB  DC = 1029 and EB  EC = 189 then what is the value of AB  AC?
Find the minimum of √(58  42x) + √(149  140√(1  x^{2})), where 1 <= x <= 1.
Put three congruent triangles inside a unit square so that they don't overlap one another.
What is the maximum possible area of one of the triangles?
66, 78, 93, 105, 111, 114...
Consider the 5 numbers above.
Evaluate the next 3 numbers.
8,9,2,0,1,5 ...
To get all ten digits you have to add 3,4,6 and 7.
Just so, but in what order?
Prove that all numbers of the form 12008, 120308, 1203308, ... are divisible by 19.
The sum of all divisors of this semiprime number is 2696.
What is the number?
Bonus: What if the word "semiprime" was erased from the puzzle?
A cube on a table has edge length 24. A plane intersects the cube's four vertical edges at points A, B, C, and D such that point A is a vertex of the cube lying on the table. The heights of points B and C from the table floor are 7 and 12, respectively.
Calculate the volume of the portion of the cube that lies underneath the cutting plane.


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