# Monthly Archives: December 2013

## Puzzle | Num3er 2014

Older post:   Puzzle | Num3ers 2013 and 2014     2014   has   8 divisors: 1     2     19     38     53     106     1007     2014 Sum of divisors:      3240   2013,   … Continue reading

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## Puzzle: X in base 8 and Y in base 9

X  is a 4-digit number in base 8 Y  is a 4-digit number in base 9 such as Y base-9  –  X base-8  =  1 DigitSum(Y)  –  DigitSum(X)  =  1   Find  X  and  Y   For example, 3056 … Continue reading

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## Num3er 371

Tweet:   371 years ago today, the great Isaac Newton was born via @CoolR1a @grahamfarmelo Newton, Sir Isaac (1642–1727)                                                    ——————————————   371   has 4 divisors:        1     7     53     371 Sum of divisors:        … Continue reading

## Puzzle| Sequence of repdigits: as simple as 1,2,3

1 (1+2+1) = 2^2 (1+2+3+2+1) = 3^2 (1+2+3+4+3+2+1) = 4^2 (1+2+3+4+5+4+3+2+1) = 5^2 (1+2+3+4+5+6+5+4+3+2+1) = 6^2 (1+2+3+4+5+6+7+6+5+4+3+2+1) = 7^2 (1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) = 8^2 (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 9^2 121 = 11^2 121*(1+2+1) = 22^2 121*(1+2+3+2+1) = 33^2 121*(1+2+3+4+3+2+1) = 44^2 121*(1+2+3+4+5+4+3+2+1) = … Continue reading

## Janken (rock-paper-scissors) Robot with 100% winning rate

## Integers such that N^5 = A^5 + B^5 + C^5 + D^5 + E^5

(1)   A^5   =   B^5   +   C^5   +   D^5   +   E^5   +   F^5   For example,       72^5   =   67^5   +   47^5   … Continue reading

## Puzzle| Factorial of digits of prime numbers (under 1000)

2-digit primes :     ab  is a 2-digit prime. Conditions : Let’s find primes such that: ab  >  a! * b! ab  –  (a! * b!) ab  +  (a! * b!) ab * a! * b!  –  1 … Continue reading

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

## Puzzle | Num3ers 2013 and 2014

Find smallest integers  (x, y)   so that 2013*x  is square,    2014*x  a cube, and 2013*y  is a cube,    2014*y  a square

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

## 4-digit number abcd = (k+a)(k+b)(k+c)(k+d)

abcd  =  (k + a)(k + b)(k + c)(k + d) abcd  is a 4-digit number and  k  is a positive integer.   For example, k = 5 1500  =  (5 + 1)(5 + 5)(5 + 0)(5 + … Continue reading

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## 2-digit numbers whose cube can be expressed as the sum of cubes

6^3  =  3^3  +  4^3  +  5^3 12^3  =  6^3  +  8^3  +  10^3  =  3^3  +  4^3  +  5^3  +  8^3  +  10^3 13^3  =  5^3 + 7^3 + 9^3 + 10^3  =  1^3 + 5^3 + 6^3 … Continue reading