We extend the deadline for solutions until September 22.
Hints for the 2 symmetric solutions known so far to the 10x10 design:
1. Each corner of the 10x10 square belongs to a different room.
2. Each 1x1 cell of the central 2x2 square belongs to a different room.
Can you find them both...
Oh, in case you were wondering: at least 1 solution exists to the 10x10 design. I will post it on September 2, unless someone can find it first...
Good luck!
SPECIAL PROJECT:
Our square-headed architect would definitely prefer museum designs with some sort of symmetry, in addition to the rest of requirements (splitting the nxn square into n-polyominoes, all with the same perimeter and the same number of neighboring rooms), so we are also putting...
You are right. The statement did not clarify -but should have- that the idea is to use shapes for the rooms made up by joining n 1x1 squares side by side (a.k.a. n-polyominoes). That was the purpose of stating that the side length of the complex is an integer.
Please introduce this constraint...
HINT:
Here is a technique that may help produce new solutions:
1. For each value of n that you choose to investigate, construct or look up regular graphs on n vertices with degree > 2 that can be drawn without crossings between edges (i.e., with edges meeting only at vertices).
2. For each...
This puzzle is about a square-headed architect who is designing a museum in the shape of an nxnxh square box, where n is an integer denoting the side length and h is the height of the building.
Building design is subject to the following additional constraints:
1. For any n chosen there will...
Let´s call A the prisoner who deduced he had a dot on his hat and let me reproduce his reasoning. A thinks: If I didn´t have a dot on my hat, B would have seen 1 dot in total and he (B) would have deduced that because C has not spoken, C has not seen zero dots. Therefore, I (A) having no dot and...
Conjecture: Consider any group with an even number of people where each member is connected to any other through some chain of people. Then the original group can be split into groups where each member knows an odd number of people directly.
Note: If the party is such that each member knows an...
An algebraic number is a number that is a root of a non-zero polynomial in one variable with rational (or equivalently, integer) coefficients. Numbers such as pi that are not algebraic are said to be transcendental and ¨almost all¨ irrational numbers are transcendental.
Since pi is not a root...
Unbelievable! (read ¨Unbelievable factorial¨) Looks like there is some truly urgent need for foolproof factorial control measures - to prevent those less-than-competent screen editors from confusing the heck out of those among us who strive, day in and day out, to make proper use of this...
True, although some of us still prefer to say ¨Wow factorial¨. However, I must say in our defense that we do write ¨Wow!¨ like the rest of the world:smile: