# 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

## 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

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## 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

## 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

## Sum of Consecutive Prime Numbers Under 1000

List of all prime numbers under 1000: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, … Continue reading

## 2 puzzles: Squares, Cubes & Prime Numbers

(1)   Sum of the squares of the digits of a prime is another prime number For example,   11,   1^2 + 1^2 = 2 is prime the prime number   23,   2^2 + 3^2 = 13 the … Continue reading

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## Expressing Prime Num3ers by Using All Digits 1,2,3,4,5,6,7,8,9

Expressing Prime Num3ers using all digits from 1 to 9 only once From 1 to 9: (-1) + 2 – 3 – (4 * 5) + (6 * 7) + 8 + 9 = 37   is a prime number … Continue reading

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## When Sums of Products of Prime Num3ers is a Power

A primorial, denoted n#, is the product of the first n prime numbers. The first 15 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 1# = 2 2# = 2*3 = … Continue reading