Challenge Math and Brain Teaser Problems!

I have a large book with like 1000 brain teasers and puzzles. I will post some of them here later.

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Here is the first riddle. This one is quite easy, in my opinion. (Rated difficulty 6 in the book)

Three models, Miss Pink, Miss Green and Miss Blue are on the catwalk. Their dresses are pink, green, and blue.

"It's strange," Miss Blue remarks to the others. "We are named Pink, Green and Blue, and our dresses are pink, green, and blue, but none of us is wearing the dress that matches her name."

"That is a coincidence," says the woman in green.

From that information, can you determine the colour of each model's dress?

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Hmmmm... is it Pink is wearing green, blue pink, and green blue? That's assuming the two speakers were different.

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Dang it. You just beat me to it. I was just gonna say that.

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do we assume that the models can only see the other models' dresses, or that they can see their own, too?

and are we assuming here that the models all have functioning logical thinking capabilities?

EDIT: OOPS USED THE WRONG APPROACH THIS QUESTION DOESN'T NEED THAT LEVEL OF METAQUESTIONING

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okay i way overthought that haha

answer: miss blue is wearing pink, miss green blue, and miss pink green.

my steps for anyone who's just too tired and wants a quick answer to the question w/o stressing

my initial approach was "look at what each model could see the others wearing, and from there figure out what each model is thinking". way, way overthought the problem.

the correct and easier approach, however, was to look at the discussion.

1): miss blue cannot be wearing green, as the person replying to her is wearing green.

therefore, we are left with two things miss blue can wear: pink, and blue. and, of course, miss blue can't wear her own color, so she must be wearing pink.

2) the person wearing green can't be miss green or miss blue

miss green can't wear her own color, and miss blue is wearing pink, as said above. therefore, we are left with one choice: miss pink must be wearing green!

3) process of elimination

we are left with one more person and one more dress: miss green and the blue dress.

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Ooh!

I know of using a table that can help with larger problems with these similar ideas:

I have more problems on this thread^ at home

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I'm not gonna look at any answers
I want to solve it

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Correct, @XiaoMiaoMi, @Petrichor and @t1_hopscotch!

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Here is another one that I am still in the process of solving.

On every birthday since I was born, I have had a birthday cake decorated with the appropriate number of candles. So far I have blown 210 candles. How old am I?

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This is eaaaasssssyyyyy

The person in the riddle is 20 years old.

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This has to do with triangle, numbers! Awesome!

This is a great question, and has to do a lot with triangle numbers!
First, I'll explain what they are: a triangle number is like a factorial (n!), but instead of multpliyong together all the previous numbers, you add them together.

There's a formula for finding triangular numbers, which is derived form the patter of 1, 1 + 2, 1 + 2 + 3, ...
It follows a right triangle using dots (I'll provide a link for this!)

n * ( n + 1 )
–––––––
2

Now that we are talking about it, this is why square numbers are called square! It makes a square pattern when you increase which gives you the formula:

n*n

Also! A square number can be trianglular! Can you find any examples??

Lastly, there are numbers such as pentagonal, hexagonal, septagonal, ... , myriagonal!
Here's links to these that explain them better:

Hope this helped! This stuff is great!

20 years

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A man is trapped in a room. The room has only two possible exits: two doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon. How does the man escape?

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Ok, correct. How many candles would you have blown if you are 87? :P

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I've heard this before, but I don't remember the answer!

There are no windows, so how can the magnifying glass magnify anything??

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One of the rooms is made from magnifying glass.

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(87*(88) / 2

=

3828 candles

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