# Monthly Archives: June 2013

## Sum of four consecutive cubes is a square

(x – 1)^3   +   x^3   +   (x + 1)^3   +   (x + 2)^3 =   4*x^3   +   6*x^2   +   18*x   +   8   we want this sum … Continue reading

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## Sum of two Triangular Numbers

Definition: http://mathworld.wolfram.com/TriangularNumber.html   Let T(1) and T(2) be two triangular numbers T(1)   =   (a^2 + a)/2 T(2)   =   (b^2 + b)/2 Let n be the sum n   =   (a^2 + a)/2   + … Continue reading

## Primes in a Circle

Place the numbers 1 to 14 around a circle so that both the sum and the (positive difference) of any two neighboring numbers is a prime. Source:    wordplay.blogs.nytimes

## Patterns | Perfect Num3ers in bases 2, 3, 4

A perfect number is a positive integer that is equal to the sum of its proper positive divisors. http://mathworld.wolfram.com/PerfectNumber.html   in base 10: 6 28 496 8128 33550336 8589869056 137438691328 2305843008139952128 2658455991569831744654692615953842176 191561942608236107294793378084303638130997321548169216   Note the patterns,   when … Continue reading

## Num3er 2013 | N^2 = a^3 + b^3 + c^3 – 3abc

N^2   =   a^3   +   b^3   +   c^3   –   3abc   2013^2   =   (-714)^3   +   100^3   +   617^3   –   3(-714)(100)(617) 2013^2   = … Continue reading

## Logic puzzle #Mensa | Card puzzle

Puzzle: Each card has a letter (consonant or vowel) on one side, and a number (odd or even) on the other side. Rule: If there’s a vowel on one side of the card, there’s always an odd number on the … Continue reading

## Palindromic primes | Equalities

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, 139, 149, 151, … Continue reading

## Pattern | Num3er 84

84 can be expressed as a sum of 8 consecutive numbers in descending order: 84   =   14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 and 14 + 13 + 12 … Continue reading

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## Num3er 162

Pat’s blog asks:   162 is the smallest number that can be written as the sum of 4 positive squares in 9 ways. Can you find all nine ways?   162   can be expressed as the sum of … Continue reading

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## Multiplication puzzle #2

Older post:    Multiplication puzzle #1   In this multiplication, each digit from 0-9 appears exactly 2 times. N.B.    No leading zeros in any number.                       ? ? ?                  *   ? ? ?                    ———–                        … Continue reading