Interesting Math Problems

[Animal]

Yep. The answer is 30.906250.

[Animal]

Let's say there is a basket. And inside the basket are twelve balls. Five of the balls are white. And Seven of the balls are black.

Now, each time you draw out a ball, you note what color it is and then you replace it. As you replace it, you also add back 2 more balls that are the same color. You do this each time you draw out a ball.

What are the odds (your answer must be a fraction or ratio in its lowest denominator) that you drew out a black ball, then drew out another black ball, then drew out a white ball, and then drew out another white ball?

[QillerDaemon]

Yep. The answer is 30.906250.

Well, yes you're "right", but this is an olympiad question. They don't want a numerical answer, they want to see you go thru the effort to show a rational form of the right answer. That involves going thru expansions and substitutions to arrive at rational sub-answers, which you'll use for further expansions and substitutions, until you come to the rational answer.

That is to say, besides X² + Y² = 2, what else is it equal to? What is X³ + Y³ equal to? What are the patterns as you go up the exponents? Once you arrive at those intermediate formulas, what can you use to simplify them?

The "correct" answer is actually X¹¹ + Y¹¹ = 989/32. You'll come to this once you figure out what X⁵ + Y⁵ and X⁶ + Y⁶ are equal to.

But geeez, you really want me to go thru all that?!

[Bluespruce1964]

4 - 3 + 10 / 5 * 2 =

[Animal]

4 - 3 + 10 / 5 * 2 =

-3

[Animal]

Yep. The answer is 30.906250.

Well, yes you're "right", but this is an olympiad question. They don't want a numerical answer, they want to see you go thru the effort to show a rational form of the right answer. That involves going thru expansions and substitutions to arrive at rational sub-answers, which you'll use for further expansions and substitutions, until you come to the rational answer.

That is to say, besides X² + Y² = 2, what else is it equal to? What is X³ + Y³ equal to? What are the patterns as you go up the exponents? Once you arrive at those intermediate formulas, what can you use to simplify them?

The "correct" answer is actually X¹¹ + Y¹¹ = 989/32. You'll come to this once you figure out what X⁵ + Y⁵ and X⁶ + Y⁶ are equal to.

But geeez, you really want me to go thru all that?!

Wow, you never fail to tell me i have the right answer but put a disqualifier on it as though its wrong.

if you want to see the long version, then its 31,648 + (18,272 * sqrt(3)) - 31,648 - (18,272 * squrt(3)) / 2048.

which reduces to (31,648 + 31648)/2048 or 63,296/2048. Now, factoring that down we get 31,648/1024 = 15,824/512 = 7,912/256 = 3956/128 = 1978/64 = 989/32. which is as low as you can go.

[Bluespruce1964]

4 - 3 + 10 / 5 * 2 =

-3

Isn't is PEMDAS?

4-3+4= 5?

It's been 36 years since I've taken a math class, but I think I still remember how.

[Animal]

4 - 3 + 10 / 5 * 2 =

-3

Isn't is PEMDAS?

4-3+4= 5?

It's been 36 years since I've taken a math class, but I think I still remember how.

Honestly, I don't know. The way I learned you did Multiply and Divide first in whatever order they came from left to right. Neither Multiply or divide took priority over each other, only how they read left to right. Next Plus and Minus the same way.

The reason I was given at the time was that if there was a reason why you MUST multiply 5*2 before you divide 10/5 then you would use parenthesis to emphasize what goes first. Without parenthesis, you read the equation left to right and solve Multiplication and division first, then add and subtract.

So, this problem becomes 4 - 3 + 2 * 2 = 4 - 3 + 4 = 5. which I got it wrong the first time. I don't know what I did.

Yes, you are right.

[Antknot]

4 - 3 + 10 / 5 * 2 =

order of operations is Multiply, divide, add, subtract

so it becomes
4 -{3 + [10 / (5 * 2)}}
4 - {3 +[ 10 / 10]}
4 - { 3 + 1}
4 - 4
0

[QillerDaemon]

4 - 3 + 10 / 5 * 2 =

-3

This is the answer you get if you use C operator precedence. Mult/Div then +/- in left to right order.

Other programming languages will give different answers, since they use a different operator order.
MUMPS (DSM) will give an answer of 4.4, GWBasic will give 0.

That's why there is no answer to this problem. Even mathematicians will disagree on precedence.

[QillerDaemon]

[Antknot]

[Animal]

Hefner's formula was always to divide your own age by 2 and then add 7. No matter what age you are.

[Bluespruce1964]

If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

[Animal]

If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

a nickle.

[Antknot]

If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

..050

Assuming no tax

[Deathproof]

What is the next number in this sequence:

3, 13, 1113, 3113, 132113, 1113122113, __________

[stonedmegman]

42

[Animal]

311311222113

[Deathproof]

311311222113

Good job.

[Animal]

311311222113

Good job.

How high would you have to continue this sequence before one of the numbers became a "4"?

[Deathproof]

311311222113

Good job.

How high would you have to continue this sequence before one of the numbers became a "4"?

Hmmm... good question. Let's try it out. The next number in the sequence would be 13211321322113. Your turn.

[Animal]

311311222113

Good job.

How high would you have to continue this sequence before one of the numbers became a "4"?

Hmmm... good question. Let's try it out. The next number in the sequence would be 13211321322113. Your turn.

1113122113121113222113. your turn.

[Deathproof]

311311222113

Good job.

How high would you have to continue this sequence before one of the numbers became a "4"?

Hmmm... good question. Let's try it out. The next number in the sequence would be 13211321322113. Your turn.

1113122113121113222113. your turn.

31131122211311123113322113

[Animal]

311311222113

Good job.

How high would you have to continue this sequence before one of the numbers became a "4"?

Hmmm... good question. Let's try it out. The next number in the sequence would be 13211321322113. Your turn.

1113122113121113222113. your turn.

31131122211311123113322113

132113213221133112132123222113