Monthly Archives: April 2013

#puzzle | Base 9 — Part 3

Note the pattern: Base 9                                      Base 10 210                             … Continue reading

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#Puzzle | Bases less than 10 – digit reversals — Part 2

Find, for each base system less than 10 (bases 2 to 9), every instance of a number formed of two different non-zero digits that is a multiple of the number obtained by interchanging the digits.           … Continue reading

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#Puzzle | Base 7 — (Part 1)

There’s a unique 4-digit number in base 10   that can be converted into its equivalent in base 7   by interchanging the left hand and right hand digit pairs. Find it.     @mikeandallie and @InfinitelyManic : 1234   … Continue reading

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lcm(a,b,c,d) = a+b+c+d

Definition: Least common multiple http://en.wikipedia.org/wiki/Least_common_multiple http://mathworld.wolfram.com/LeastCommonMultiple.html                                                    ——————————————   Goal:   To find four positive integers   a, b, c, d   such that   LCM (a, b, c, d) = a + b + c + d Irreducible … Continue reading

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Powers | 5^n

  n           5^n 1                 5 2                25 3                125 4       … Continue reading

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Num3ers of the form 3^n – 2^n

“Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.” ~ Paul Erdös                                                       ——————————————-   … Continue reading

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Concatenation | Appending and Prepending the digits 1 and 3 to a string

17   —–>   1173 1173 ——–   =   69   17 59   —–>   1593 1593 ———-   =   27   59 769231   —–>   17692313 17692313 —————–   =   23   769231   … Continue reading

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Common digits : N and N^2

The smallest integers N, such that N and N^2 share the same digits are: 1 digit in common : 5^2   =   25 6^2   =   36 2 common digits : 11^2   =   121 25^2   … Continue reading

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Odd Num3ers less than 100 in base 11

Take an odd number less than 100 and multiply it by 95 95 * 1  =  95 95 * 3  =  285 95 * 5  =  475 95 * 7  =  665 95 * 9  =  855 95 * 11 … Continue reading

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Concatenation | Appending and Prepending the digits 2 and 1 to a string

3  —–>  231                                                                            … Continue reading

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