# Category Archives: Number Puzzles

## 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

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## Primes p; n(p + n) is a square

Consider the first few prime numbers:           2,   3,  5,  7,  11,  13,  17,  19,  23,  29,  31,  37 And   f(p) = n(p + n),     where  p  is an odd prime and … Continue reading

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## 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

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## Concatenation | (x – y + z)^3 = x || y || z

Older post:   Concatenation: x||y||z = x^3 + y^3 + z^3   Find integers   x,   y   and   z   such that                                                  (x – y + z)^3   =   x || y || z                                                  … Continue reading

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## Using Primes 2,3,5,7 only once to make 1-100

Game: You can use the primes   2, 3, 5, 7   and the basic operations   +, -, *, /   and   !   (factorial) only once to make numbers from   1   to   100.   … Continue reading

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## 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

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## 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

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## Concatenation| Sum of consecutive integers

Goal:   To find integers that are the sum of consecutive integers in the number   For example, 19 || 0 = 190 = 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1+0   20 || 4   =   204   =   20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4   21 … Continue reading