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

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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(x-1) + … Continue reading

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When Odd Powers of Num3er End with the Same Num3er

Take for example 251, Its odd powers: 251^1 = 251   251^3 = 15813251   251^5 = 996250626251   251^7 = 62764785704439251   251^9 = 3954244264165377252251   251^11 = 249121342886682932269065251   251^13 = 15694893723203911415883379878251   251^15 = 988793999455569623112068815709691251   251^17 … Continue reading

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Diophantus’s Riddle

Diophantus of Alexandria: Biography http://www.gap-system.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

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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

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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

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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

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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

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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