# Some interesting brainteasers Starter I used

• ƒ(x) → ∞
In summary: I'll leave it up to the experts.They are equivalent. Graphing exactly is... complicated. I'll leave it up to the experts.
ƒ(x) → ∞

Some interesting brainteasers

Starter

I used factorials for this one, but it will be interesting to see how you attempt your answer.

These questions are designed so that anybody above the age of about 13 can answer them without much mathematical experience.

If this is a success then I will reveal the answer this time next week and come up with a new one [MONDAY 28TH DECEMBER 2009]

ƒ(x) → ∞ said:
I used factorials for this one
Brainteasers factorial?

ƒ(x) → ∞ said:
I used factorials for this one

I thought he might mean: 1!

DaveE

Am i missing something? what's the brainteaser?

ƒ(x) said:
Am i missing something? what's the brainteaser?
That's the brainteaser.

jimmysnyder said:
That's the brainteaser.

Oh, I assumed that there was some math problem that i was missing.

There is something missing. The problem is, what is the problem?

D H said:
There is something missing. The problem is, what is the problem?

Thats what i said.

And for the ladies, it's in the same place.
48
8

ƒ(x) said:
I found the question:

jimmysnyder said:
And for the ladies, it's in the same place.
48
8

How did you do this?

Borek said:

Considering how I wasn't sure about how to do the questions

ƒ(x) said:
How did you do this?
For the first one, I counted. I did use a factorial, but it wasn't a big part of the solution.
For the second one, I graphed a few points and the figure appeared.

jimmysnyder said:
For the first one, I counted. I did use a factorial, but it wasn't a big part of the solution.
For the second one, I graphed a few points and the figure appeared.

What was your factorial (my teacher for pre-calculus didnt teach)?

For the second, doesn't the function go to infinity?

The second one is pretty much 4 triangles in the four quadrants with vertices
(-2,0),( 0,2) ,(0,0)

(2,0),( 0,2) ,(0,0)

(0,-2),( 0,0) ,(2,0)

(0,2),( 0,0) ,(2,0)

The area is simply ( 0.5(2)(2)) *4 = 2*4 =8

In how many ways can the product of the numbers so that the numbers equal 36?

Wow, I have even no idea what it does mean and Jimmy was able to solve.

Edit: what do we know about colors assigned to dices? What color is four sided dice? Six sided one? Ten sided? Twelve sided? Twenty sided? Not sure what types I had, I can't find my set form RPG times.

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╔(σ_σ)╝ said:
The second one is pretty much 4 triangles in the four quadrants with vertices
(-2,0),( 0,2) ,(0,0)

(2,0),( 0,2) ,(0,0)

(0,-2),( 0,0) ,(2,0)

(0,2),( 0,0) ,(2,0)

The area is simply ( 0.5(2)(2)) *4 = 2*4 =8

It is? http://www.wolframalpha.com/input/?i=|y-x|+|y|+=+2

Borek said:
Wow, I have even no idea what it does mean and Jimmy was able to solve.
For instance, you could roll a red - 1, orange - 2, yellow - 3, and purple - 6. The product is 36. That's 1, now go find the other 47.

red - 12, orange - 1, yellow - 3, purple - 1. Now I need only 46.

jimmysnyder said:
For instance, you could roll a red - 1, orange - 2, yellow - 3, and purple - 6. The product is 36. That's 1, now go find the other 47.

I attempted it by finding combinations of 4 whose product is 36 (assuming that they were all 6 sided dice).

I think i got:

1,1,6,6
1,2,3,6
1,3,3,4
2,2,3,3
1,3,3,4

I might have missed one combination. But, since there are 4 identical dice, each one could fill one of the spots. So wouldn't it be 4!*5? Which is 120

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ƒ(x) said:
I attempted it by finding combinations of 4 whose product is 36 (assuming that they were all 6 sided die).

I think i got:

1,1,6,6
1,2,3,6
1,3,3,4
2,2,3,3
1,3,3,4

I might have missed one combination. But, since there are 4 identical dice, each one could fill one of the spots. So wouldn't it be 4!*5? Which is 120
For one thing, you have 1,3,3,4 listed twice. For another, consider the first one 1,1,6,6. In this case I counted yellow-1 purple-1 the same as purple-1 yellow-1 but you counted them as different.

jimmysnyder said:
For one thing, you have 1,3,3,4 listed twice. For another, consider the first one 1,1,6,6. In this case I counted yellow-1 purple-1 the same as purple-1 yellow-1 but you counted them as different.

Oh, I did. So its back to 96. Why would you count them the same?

ƒ(x) said:
Oh, I did. So its back to 96. Why would you count them the same?
Because I can't tell the difference between them just by looking. One yellow die and one purple die look just like one purple die and one yellow one. How do you propose to tell them apart?

jimmysnyder said:
Because I can't tell the difference between them just by looking. One yellow die and one purple die look just like one purple die and one yellow one. How do you propose to tell them apart?

Good point. The problem was asking for different outcomes, not total outcomes. 48 it is.

ƒ(x) said:

They are equivalent. Graphing exactly is more complicated.If you switch x and y in the original equation you can see my train of thought.

And no the graph does not go to infinity, the graph plotted is not for all values of x and y.

At x=2 or -2 y must be 0 or 2.

If you graph this completely you get some sort of parrallelogram.You get 2 triangles with vertices

(-2,0), (2,2),(2,0)
(2,0), (-2,-2),(2,0)
http://www.wolframalpha.com/input/?i=|y-x|+|y|+=+2,+++-7<+x++<+7,+-2<+y++<+2Again you can see my train of thought by rotating the parralelogram such that the the point (2,2) is on the y axis.

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Effectively, you can solve by realizing that a function with an absolute value is basically taking TWO functions, one negative, one positive. So, for:

y = |x|

You can graph both:

y = x
y = -x

And that'll give you the basic shape-- you just know that y is always positive, so some areas of the graphs are invalid. With this problem, it's 4 equations:

|y - x| + |y| = 2

A) y - x + y = 2
B) y - x - y = 2
C) -y + x + y = 2
D) -y + x - y = 2

Which simplify to:

A) y = x/2 + 1
B) x = -2
C) x = 2
D) y = x/2 - 1

That's enough to solve the problem, even without invalidating the ranges, which isn't too hard to do. It encloses a parallelogram, whose area is pretty simple to determine.

DaveE

1,1,6,6 - 6 ways of getting this
2,2,3,3 6 ways of getting this
1,2,3,6 - 24 ways of getting this
1,3,3,4 12 ways of getting this

Therefore the answer is 12+24+6+6 = 48 ways

8

## What are some interesting brainteasers?

Some interesting brainteasers may include puzzles, riddles, and logic problems that challenge one's thinking skills and creativity. They often have multiple solutions and require thinking outside of the box.

## How can brainteasers be used in a starter activity?

Brainteasers can be used as a fun and engaging way to kickstart a lesson or meeting. They can help to stimulate critical thinking and problem-solving skills, and can also serve as an icebreaker to get people talking and interacting with one another.

## What are the benefits of using brainteasers in a starter activity?

The use of brainteasers in a starter activity can help to promote teamwork, improve cognitive abilities, and boost creativity and imagination. They can also be a great way to introduce new concepts and ideas in a fun and interactive manner.

## How can I create my own brainteasers?

To create your own brainteasers, you can start by thinking of a problem or scenario and then coming up with unique and creative solutions. You can also use existing brainteasers as inspiration and add your own twist to make them more challenging and interesting.

## Are there any resources for finding new brainteasers?

Yes, there are many resources available for finding new brainteasers. These include books, websites, and apps specifically dedicated to brainteasers and puzzles. You can also find brainteasers on social media platforms or by joining online communities that share and create brainteasers.

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