Monthly Archives: March 2012

3X3 Grid Digits 1 to 9

To arrange the digits 1 to 9 in the 3×3 square in such a way that the number in the second row is twice that in the first row, and the number in the bottom row is three times that … Continue reading

Challenge #2 : Number Theory / Geometry

The lenghts of the sides of an isosceles triangle are integers, and its area is the product of the perimeter and a prime. What are the possible values of the prime?

A Fun Little Puzzle: 3X4 Grid 1 to 12 numbers

1     2      3     4 5     6      7     8 9    10   11   12 Object: To divide this grid into two parts so that the total sum … Continue reading

Arranging Digits from 1 through 9 in Two Groups

The digits 1 through 9, are arranged in two groups. Each group represents a multiplication and, more interestingly, results in the same product 532                                76 … Continue reading

Interesting Trigonometry Identities

I’m going to list trig. identities that I find interesting. I leave the proofs for the readers. I start with these two: (1)   If   α, β and γ   are the angles of a right triangle, then sinα … Continue reading

Challenge #1 : Arithmetic Progression Question

Prove that the product of any four consecutive integer members of an arithmetic progression may be expressed as the difference of two integer squares

If x is a Triangular number, then so is ax+b

Triangular number: Definition 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, … Continue reading

12 = 3*4 and 56 = 7*8. Other examples?

12 = 3*4   and   56 = 7*8   are of the form: 10*a + (a + 1) = (a + 2)*(a + 3) 11a + 1 = (a + 2)*(a + 3) 11a + 1 = a^2 + … Continue reading