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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Monthly Archives: April 2012
Divisibility by 7
If the number is 325, then follow 3 black arrows, then 1 white arrow, then 2 black arrows, then 1 white arrow, and finally 5 black arrows. If you end up back at the white node, n is divisible … Continue reading
Subtractions of Num3ers of the form abc – cba
abc – cba 100*a + 10*b + c – 100*c – 10*b – a = 99a – 99c (1) If a = x, b = x – 1, c = x – 2 100x + 10(x1) + … Continue reading
Diophantus’s Riddle
Diophantus of Alexandria: Biography http://www.gapsystem.org/~history/Biographies/Diophantus.html http://mathworld.wolfram.com/DiophantussRiddle.html Diophantus’s riddle is a poem that encodes a mathematical problem. In verse, it read as follows: ‘Here lies Diophantus,’ the wonder behold. Through art algebraic, the stone tells how old: ‘God gave … Continue reading
When Sum of Two Num3ers is 999
PART 1 : 999^1 = 999, 9 + 9 + 9 = 27 = 3*9, 2 + 7 = 9 999 = 1 * 999 999^2 = 998,001 998 + 001 = 999 … Continue reading
ab  c = abc
Solving for positive integer only the equation (100*a + 10*b + c)*(10*a + b + c) = (10*a + b)^3 + c^3 we get, (1) a = 1, b = c = 0 (2) a = b = … Continue reading
Ding Yidong Magic Circles [Part 3]
Radial group 1 = 1, 11, 21, 31, 41 1 + 11 + 21 + 31 + 41 = 105 Radial group 2 = 2, 12, 22, 32, 42 2 + 12 + 22 + 32 + 42 = … Continue reading
Magic Circles [Part 2]
Eight annular rings and a central circle each ring being divided into eight cells by radii drawn from the centre; there are therefore 65 cells. The number 12 is placed in the centre, and the consecutive numbers 13 … Continue reading
Yang Hui Magic Circle [Part 1]
The sum of the numbers on four diameters 28 + 5 + 11 + 25 + 9 + 7 + 19 + 31 + 12 = 147 = (69 * 2) + 9 20 + 16 + 23 … Continue reading
3X3 & 5X4 Grids on Year Calendar
Picture a 3×3 grid around any 9 numbers of the numbers of any month on the calendar. Add them up. (1) 3X3 Grid : Let’s pick, for example, February, and the following 3X3 grid: 9 10 11 … Continue reading
Choose either 2 or 3
Multiply your chosen number by any odd number and multiply the number you did not choose by any even number. Add those two products together. From that result, how can I determine which number was chosen?