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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: August 2012
Digit Switch – 6digit Num3er ABCDEF * 6 = DEFABC
Let ABCDEF be a 6digit number, and A B C D E F * 6 ——————— D E F A B C Let ABC = x and DEF = y … Continue reading
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Num3er 34,969
Count von Count loved all numbers, but 34,969 in particular. Why? http://www.bbc.co.uk/news/magazine19409960 34969 = 187^2 is a perfect square. 187^2 = 11^2 * 17^2 187 = 11 * 17 (the product … Continue reading
Num3ers expressed as the sum of 4th and 5th powers of their digits
1634 = 1^4 + 6^4 + 3^4 + 4^4 8208 = 8^4 + 2^4 + 0^4 + 8^4 9474 = 9^4 + 4^4 + 7^4 + 4^4 4150 = 4^5 … Continue reading
(x, y); x + y = a^2 and x*y = b^2
Goal: To find (x, y) such that … the sum is a square: x + y = a^2 the product is a square: x * y = b^2 For example, (1) x = 2 … Continue reading
Math Food – Shapes and Patterns
Fruits of a Kousa Dogwood tree MAA Found Math Gallery http://maa.org/FoundMath/11week38.html Pi Pie Möbius Strip Bagel Sierpinski Carpet Cookies Fractal Snowflake Cupcakes Menger Sponge Gingerbread House … Continue reading
Puzzles: Use operators +, , *, / write an expression equal to a num3er
(1) Use the four digits 3, 3, 7, 7 and +, , *, / to make 24 (2) Use +, , *, / and the digits 1, 2, 3, … Continue reading
Rob Bryanton’s Imagining the Tenth Dimension
Imagining the Tenth Dimension (annotated) “Rob Bryanton’s Imagining the Tenth Dimension is one of the most brilliantlyconceived and mindstretching books that I’ve ever encountered. Bryanton presents a uniquely compelling model of our 10dimensional universe, that allows one to … Continue reading
AB = AB; AB * (A+B) = A^3 + B^3
I set out to solve the two equations (10*X + Y)(X + Y) = X^3 + Y^3 (100*X + Y)(X + Y) = X^3 + Y^3 and I got the following solutions: Trivial solutions: a = 0, … Continue reading
Numbers and Their Reversion
9 + 9 = 18 9 * 9 = 81 24 + 3 = … Continue reading
Division: AHHAAH / JOKE = HA
AHHAAH ————— = HA JOKE where each letter represents a digit. Find the numbers.