The Enigma Plaza

Welcome, this is a place where you can relax and hopefully enjoy yourself. If you enjoy puzzles and problem solving then this is the place to be. Located here are puzzles of all sorts; ranging from simple word puzzles to the truly arcane. There is something for everyone. All that is required is for you enjoy your stay :)

As LL put it, to get the ball paradiddling, a simple cipher for you to decipher: IBWF B Ojdf Ebz!

Feel free to submit your own puzzles, maths problems, riddles etc. it can be anything really. Also, any answers should be keep hidden for the sake of others. I'll update as required.

Express log9 xy in terms of log3 x and log3 y. Without using tables, solve for x and y the simultaneous equations

log9 xy = 5/2

log3 x log3 y = -6

expressing your answers as simply as possible.

Find the best move for white

Brothers Alfred, Benedict and Cyril are asleep in their cell, when the novice Legpulla sneaks in and paints a blue bob on the top of each of their shaven heads. When they awake, each notices the blob on the other's head. Now, the monastery rules are clear: it is impolite to say anything that will cause direct embarrassment to another member of the order, but it is also impolite to conceal anything embarrassing about yourself. And impoliteness is not permitted under any circumstances. So the monks say nothing, and their demeanour gives no hint of what they have seen.

Each vaguely wonders wether he, too, has a blob, but dare not ask, and there are no mirrors in their cell, nothing reflective at all. And so things remain until the Abbot enters, frowns, and informs them that 'At least one of you has a blue bob on his head.'

Of course, all three monks know that. So does the information make any difference to them?


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3/4. But you know we have social groups for this kind of thing? Have a look through them, and you might even find some like this/that you like.
Really, thats the first i've heard of it. Thanks for the advice :)

E: Might you point me in the right direction?
“Because it can produce a few notes, tho they are very flat; and it is never put with the wrong end in front!”


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the raven one actually doesn't have an intended "answer", but carroll kinda invented that answer afterward

it is historically quite contentious, look it up!!
A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet nine inhabitants: Mel, Bart, Sue, Betty, Rex, Zeke, Sally, Zoey and Homer. Mel claims that only a knave would say that Sally is a knave. Bart claims, `Rex is a knave.' Sue says that Mel and Homer are knaves. Betty tells you, `I know that I am a knight and that Sally is a knave.' Rex says, `Betty and I are both knights.' Zeke tells you that at least one of the following is true: that Sally is a knight or that Sue is a knight. Sally says, `It's false that Betty is a knave.' Zoey says, `It's not the case that Sue is a knave.' Homer tells you that Betty is a knave or Zeke is a knave.


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Find the best move for white

I looked at this for a while. There isn't really a move that will incapacitate black, or put him into pressure that he can't get out of safely. I'd say the best move for white, one that has the highest potential for black casualties and the lowest risk for white casualties, would be to move the pawn at e3 up to e4. His next move he will do one of two things: Take that pawn with his d5 pawn, or leave it and do something else. If he leaves it alone, you will of course be able to take the d5 pawn with your pawn and threaten his queen and knight, forcing him to choose. If he takes the pawn with his d5 pawn, you can move your rook (d1) in between his knight and his queen (d6). This will of course force him to move his queen, because if his queen takes your rook you will easily be able to take his queen with your own. At this point there are several safe places to move his queen, but only a couple that will allow her to remain in reasonable position to protect her king. To stay in play, black will likely move his queen to either e7, f7, or g8. From here, your endgame strategy will depend on where black moves his queen to. If she moves to e7 or g8, use your bishop to take the pawn at f6. This will simultaneously check the king and threaten the queen, forcing black to choose and put you within a couple moves of checkmate. If the queen moves to f7 instead of the other two options, you will need to take the f6 pawn with your ROOK, not your bishop. The reason for this is you want to maintain the ability to force his queen to move rather than attack. She will then have to move to e7 or g8, which you will simply follow up by moving rook to f7. Once again he will have to choose between king and queen, and will put you within a few short moves (hopefully) of checkmate. I'm assuming in these scenarios that white will be smart enough to finish properly after getting rid of black's queen. There are entirely too many scenarios to list, but this move I think is the best way to put white in position to win.
Considering the fact that you are only allotted one move, the best move is Bishop to F6 because it's the only one that gives you offensive momentum
For chess I'd say Queen to C7 since it nets a free Pawn, possibly two while also pinning the Knight and keeping the King under pressure.

For the logic one in the OP, yes, this information makes a difference as it confirms that all three have dots as the abbot would not single out one monk for having a dot or not having a dot.

Edit: Woah, never mind this. WaterBomb's blew my answer right out of the water.
I thought I will share some things with you:

Half full=Half empty

This is considered mathematically
And also, if a mirror has nothing to reflect is it a mirror.
Full and Empty are the same in the sense that they are both all encompassing. Full is all while Empty is nothing. All and Nothing are inverses of each other and can be seen as equals in a roundabout way.

Either that or my english professor has been filling my head with useless propaganda.
I have a question. Why is OP getting away with giving his 1st year uni math's work to other people to do for him. I passed that subject. I don't want to have to do it again.


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I have a question. Why is OP getting away with giving his 1st year uni math's work to other people to do for him. I passed that subject. I don't want to have to do it again.
I think we're dealing with a mastermind here.

(I now know where to go next time I have a critical thinking question)
I managed to solve the first one on a piece of paper, only to discover many other posters have made me look like a cheat. It is 3/4, right? Can you post some more things, like riddles and such? Sideways thinking is much more fun than maths teasers. And I disagree with ILoveLisa, Maths as a subject can never be this interesting.
You haven't done uni maths. This is just plain and simple Algorithms and Problem Solving.

lol Dancing typo.
Is Uni Maths actually interesting? It's pretty hard for a person like me to get ecstatic over it. (Year 11 Maths Methods is dull enough...)

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