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evening, but surely, a warm thank you to Alexis Prudkin for their review in educ.ar (see here) ... And a very good start to the year for everyone!

Masquerade Theme Dress For Sweet 15

Journey to Planet Biplantar

One time Spock, the space traveler student of logic, came to the planet Biplantar. On this planet, as in many others visited by Spock, the whole population is divided into two groups: the truthful and the liars. The strictly true only makes statements true while lying only make false claims.

On this planet, in addition, every house has two floors, which, in a display of imagination, call lower and upper . In one plant (may be lower or higher may be, it depends on each home) live only true to the other plant, of course, live only liars. This does not mean that each is confined to a specific plant, as if they were prisoners. By contrast, those living in a plant can freely visit the other, but "live" (Moran, overnight, live) only one of two.

In villages or small towns the houses are of simple structure and any visitor always knows what floor of the house is. In large cities, however, houses may have a very complex structure, labyrinthine would say, with false steps that seem to lead to plants lacking, false windows with landscapes (gardens created by artificially high or games of mirrors), false doors and other traps for the collection so that, after a transit time for their rooms, visitors can lose track of if you are in the lower or higher (although the resident never lost and always knows where you are).

On his first day on the planet Biplantar, Spock was in a house in a small town. He had arrived an hour or two, but still had no idea who lived on each floor. At that time he saw a resident (who lived in that house, though not necessarily on the ground where they met) and after greeting him, Spock asked which group (ie, whether it was truthful or lying). The native replied:

If I said: "If there is a floor above us then I live in it", then you could deduce which group I belong.

Spock deduced from this information immediately on what the true and living plant which plant, liars. Maybe other things concluded, perhaps not. (But note that the fact that Spock has enough information to make a certain deduction does not necessarily mean that we also have.)

The questions are: Does native spoke to Spock was truthful or a liar ? What floor of the house were the two, the upper or lower? Which of the two plants lived truthful?

For each question, the challenge is either to answer or demonstrate that the information you have is insufficient to give an accurate answer.

Have fun ...

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A theorem on 0 ^ 0

Theorem: Let T a theory that speaks to the non-negative integers and their operations, if this theory is defined as 1 0 ^ 0 then there is no contradiction.

Demo: If we define a non-negative integers in the context of the theory of finite sets F (defined as the cardinal of the same sets) then the statement 0 ^ 0 = 1 can be proved as a theorem (see here.) Therefore, the finding is consistent with the theory F, ie, FU {0} ^ 0 = 1 is consistent.

Therefore, TU {0 ^ 0 = 1} is also consistent (regardless of T consistent and defines a non-negative integers), because, otherwise, the same contradiction arises in TU {0 ^ 0 = 1} also exist in FU {0 ^ 0 = 1}, but this alleged contradiction, we have seen, does not exist.

... everything else is irrational prejudice.

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Riddler in 6 by 6

The protagonist of this problem is a board of 6x6 ...

... and the goal is complete in accordance with the following rules:

1. Each of the boxes with a circle must contain a number, which can only be, in each case, a 1 or a 4. In the other boxes will not numbers.

2. At the end, there must be at least 1 and at least a 4.

3. Some of the remaining boxes contain mines (by way of help, one is already in place), others may eventually become empty.

4. boxes with circles do not contain mines or may be empty.

5. Minesweeper As in Windows, each number should indicate how many mines there are in boxes that are around him.

Have fun ....