# Monthly Archives: June 2014

## Puzzle | quadruplet (1, 22, 41, 58)

Consider the quadruplet   (a, b, c, d) = (1, 22, 41, 58) the sum of any three of them is a perfect square:     1 + 22 + 41 = 64     1 + 22 + 58 … Continue reading

Posted in Uncategorized | Tagged , | 8 Comments

## Powers of 2 puzzle

Let M be a positive integer. Rearranging the digits of M, we obtain the positive integer N. No leading zeros. Is it possible to have two different positive integer powers of 2 this way?         … Continue reading

## Puzzle | Solve a + b + c + d = n √(abcd) (positive integers)

I like this number 1281: Concatenation of   3*4 || 3^4, DigitSum(1281) = 12. First two digits:   12 1+2+8+1 = 3√(1*2*8*1)

Posted in Number Puzzles | Tagged | 2 Comments

## Puzzle | Factoring the Difference of Two Squares

——————————————

## (1^3 + 3^3 + 5^3 + …+(2n-1)^3)/(1 + 3 + 5 +…+(2n-1))

Posted in Number Puzzles | Tagged , | 3 Comments

## Heronian triangle| Area = k*(Perimeter), k is a prime number

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? Answer:     2,   3,   5   … Continue reading

## Puzzle | 8-digit Num3ers

How many 8-digit numbers are there in which every digit occurs the same number of times as the value of the digit?   e.g.   3414434,   digit 1 occurs 1 time,   digit 3,   3 times, … Continue reading

Posted in Number Puzzles | Tagged | 2 Comments

## k consecutive integers divisible by the first k prime numbers