# Tagged Questions

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### Research Topics Needed

This coming academic year a professor has asked me to find some topics that I wish to pursue to write about. The problem/topic that will be discussed doesn't have to be open, but my trouble is that I ...
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### Throw a die three times, and get maximum number of different sums.

The IBM Ponder This problem for July 2013 throws an 8 sided die 3 times, and can get 120 possible different positive integer sums. If all the faces have positive integer sides, what is the lowest ...
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### Polyonimo Tiling

I came up with the following conjecture the other day, and was wondering if the result was well-known or even true: Define $f(P)$ for a polyomino $P$ (without holes) to be the least number of total ...
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### How many partial order on a n-set?

Let $A$ be a set has $n$ element, my question is how many partial order on it? For $n=0,1$, $N_P(n)=1$ Case $n=2$, $N_P(n)=3$ Case $n=3$, $N_P(n)=19$ Is there a general formula? Update: It seems ...
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### Cube nets hexomino tilings.

I am looking for an ~12x12 rectangle (small holes and small obtrusions are okay) made entirely of cube net hexominos. It is my understanding that perfect rectangles, in general, are not possible ...
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### Tiling with polyominos

How to prove or disprove that if a polyomino tiles the plane, it must also be able to perfectly tile some larger polyomino, which also tiles the plane? A polyomino is finite set of unit squares ...
### Can 7 Hoffman-Singleton graphs cover $K_{50}$?
Three copies of the Clebsch Graph can cover $K_{16}$, the complete graph on 16 vertices. This is part of the demonstration that $\mathrm{Ramsey}(3,3,3) > 16$. The Hoffmanâ€“Singleton graph is a ...