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| 4 (Mar 27) | 3 (Mar 11) | 2 (Feb 20) | 1 (Feb 6) |
May 7, 2008
Winners:
We call an integer *lucky* if it is a sum of positive integers (not necessarily distinct) whose reciprocals sum to 1. For example, 4 and 11 are lucky: 4=2+2, 1/2 + 1/2 = 1, and 11=2+3+6, 1/2 + 1/3 + 1/6=1. However, 2, 3, and 5 are unlucky. Find all unlucky numbers.
March 26, 2008
Winners:
(undergraduate) Donald Adams
Lamia Mekha
Marzhel Pinto
Marco Fernandez
Spencer Williams
(graduate) Renee Thompson
Vince Dayes
Solve the equation (ln x)^2 - 2.5(ln x)(ln(4x-5)) + (ln (4x-5))^2 = 0,
where x and all expressions are real.
February 15, 2008
Winners: (graduate) Vince Dayes
Fibonacci Nim is a two player game, played as follows. Players
take turns removing stones from a pile (and discarding the removed stones).
They must remove at least one stone, but no more than twice what their opponent
removed immediately before. Whoever removes the last stone(s) wins, and the
first player may remove any number of stones (except all of them).
A removes 2, leaving 8
B may remove between 1 and 4, chooses to remove 1, leaving 7
A may remove either 1 or 2, chooses to remove 1, leaving 6
B may remove either 1 or 2, chooses to remove 2, leaving 4
A may remove between 1 and 4, chooses to remove 4, A wins.
January 25, 2008
Winners:
(undergraduate) Al Sison III
Robbie Chasse
Jon David
Jonathan Saavedra
Philip Tabares
Tony Tam
Parisa Tarani
(graduate) Emiliano Vega
Vince Dayes
Six chess knights are on a 3x3 board, as pictured.
Find a sequence of legal chess knight moves that end up with the diagram reversed,
(i.e. the black knights on the bottom and the white knights on the top).
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