# Category Archives: Math Beauty

## Triangle (5, 7, 8)

A triangle with sides of length   5,   7,   and   8 Perimeter   =   20 Area   =   10 √3   ~   17.3205 one of its angles measures 60 degrees: Applying the Law … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged | Leave a comment

## Using 1,2,3,4,5 only once to make 1 – 100

Game: Using  1, 2, 3, 4, 5  only once and the basic operations (+, -, * , / , !) to make all the numbers from  1  to  100   0 = 5 + 3 – (4*2/1)       … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | Leave a comment

## Non-palindrome multiplied by its reverse is a square

For example, 288   is a non-palindrome and a non-square number. Its reverse is:     Rev (288)   =   882 and, 288   *   882   =   254016   =   504^2   is a perfect … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | 1 Comment

## DigitProduct and Sum of prime factors of numbers

(1) Integers such that the sum of prime factors equal the product of the digits of those integers:   The prime factors of   18   are:                           … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | Leave a comment

## 3-digit Num3ers w/ consecutive digits

123 + 132 + 213 + 231 + 312 + 321 = 1332 (123 + 132 + 213 + 231 + 312 + 321)/2 = 666 (123 + 132 + 213 + 231 + 312 + 321)/3 = 444 (123 … Continue reading

Posted in Math Beauty | Tagged | Leave a comment

## Num3ers such that (x+1)^3 – x^3 = y^2

OEIS – A001921 0,   7,   104,   1455,   20272,   282359,   3932760,   54776287,   762935264,   10626317415,   148005508552,   2061450802319,   28712305723920,   399910829332567,   5570039304932024,   77580639439715775,   1080558912851088832,   15050244140475527879,   209622859053806301480, … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | Leave a comment

## Concatenation | N||(N+1) and N||(N-1) are squares

N || (N + 1)                                    =                                   … Continue reading

Posted in Math Beauty, Number Puzzles | | Leave a comment

## Sum of 5 consecutive num3ers is a cube

Let   (x-2),   (x-1),   x,   (x+1),   (x+2)   be five consecutive integers. (x-2)   +   (x-1)   +   x   +   (x+1)   +   (x+2)   =   y^3 5*x   = … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , , , | Leave a comment

## Concatenation | Prime Num3ers

Smallest prime which is a concatenation of n distinct primes A083427 2 23 257 2357 112573 11132357 1113223537 111317193257 11131719223357 1113171922335437 111317192232934157 11131719223293135773 1113171922329313375759 111317192232931337415743 11131719223293133741435717   A088085 2 23 239 23911 23911313 23911313353 23911313353363 23911313353363373 239113133533633733993 23911313353363373399310401 2391131335336337339931040111911 … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | Leave a comment

## Num3er 504 – Puzzle

The factors of   504   are: 1     2     3     4     6     7     8     9     12     14     18     21     24     28     36     42     56 … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | Leave a comment