Riddles

[gamecreator]

Yes. A typo. I thought of 100 even before I added 37 and 73 and long after. The actual answer is 110.

[Zathyr]

Right, 110. Wasn't much of a riddle, I know, but I figured it was better than nothing. A little mental exercise to help keep the brain in shape.

For those wondering where 110 came from, the numbers define a polynomial function, and there's a fairly simple method for these kinds of numerical sequences. It involves taking the differences, and the differences of differences, and so on until you get a constant number. Then you can add the same constant and work back up the chain to get the next in the sequence. Some of the earliest computers, difference engines, were built for exactly that purpose (but for much longer sequences).

[gamecreator]

Here is similar riddle:
12, 15, 20, 30, ...
The question is the same: what's the next number?
Bonus question: continue the sequence.

[Davecom3]

Well, it could truly begin as...
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

On the other hand, we could have some completely seperate possibilities, utilizing primes greater than 30.

On the other hand maybe the pattern begins as...

...2, 3, 6, 12, 15, 20, 30, 35, 42, 56, 63, 72, 90, 99...

[gamecreator]

It doesn't really begin, but previous number is 10.

[Davecom3]

Which means it seems to follow the dividend path pretty well, but given it doesn't truly begin, it's not based in that area.

But if it follows the same logic, 50, 90, 170, 330, 650, 1290, 2570, 5130, ((2^10)+1)*10, ((2^11)+1)*10....? That said, I'm most likely wrong in my thoughts.

[Zathyr]

I would guess the next number is 60. And if it's following the rules I think, then the number after that is [undefined] since it would involve diving by 0.

What we see fits a pattern of 60 divided by progressively smaller numbers. Prior to that there would be 60/7 and so on.

Working back towards earlier numbers, reversing the sequence, that would make it: 60, 30, 20, 15, 12, 10, 8+⁴/₇, 7+¹/₂, 6+²/₃, 6, 5+⁵/₁₁, 5, ...

[gamecreator]

Zathyr is right. There was nothing complicated.
If you use the difference method, you can see distinctive property of such sequences.

[Davecom3]

So that's why it fit the dividend pattern so well.

[Zathyr]

Next riddle is up for grabs. I'm clicking empty here.

[gamecreator]

Here is some translated riddle.

► Show Spoiler

If someone suddenly developed knowledge of russian, you can see original here

[Davecom3]

Okay, if I've got this right:
A) 2,10, 12, 15, 18
B) 4, 11,14, 17, 20
C) Not on this exam.
D) 1, 3, 6, 7, 9, 13, 16
E) 5, 8, 19

That said, if I'm right, I'm wrong depending on translation. "Why?" you might wonder. Well, because for example, in question 10 and 16, the question might be translated to demand the answer be "A)D" in both cases. But in that case, the translation of answer I used is wrong. Probably, the correct answer, therefore, becomes, "Define answer."

[gamecreator]

Almost right.

That said, if I'm right, I'm wrong depending on translation. "Why?" you might wonder. Well, because for example, in question 10 and 16, the question might be translated to demand the answer be "A)D" in both cases. But in that case, the translation of answer I used is wrong. Probably, the correct answer, therefore, becomes, "Define answer."

I don't understand what are you talking about.

[Davecom3]

Well, depending on how you see the answer, in case of 10 and 16, you can translate it to meaning they need the exact same response, "A)D" or you may translate it to meaning they need two separate responses that act upon one another "A)D" and "D)A". But from what you've said, I must conclude I had answers for 19 and 20 switched.

So, if I've got this right:
A) 2,10, 12, 15, 18
B) 4, 11,14, 17, 19
C) Not on this exam.
D) 1, 3, 6, 7, 9, 13, 16
E) 5, 8, 20

[gamecreator]

Yes, that's right. And for my translational experience, can you say how did you understand question 20?

As for question 10, so you can interpret original version. But making such assumption is highly unlikely. I think this being standardized test would imply meaning you used to solve this riddle.

[Davecom3]

I was thinking Barometer was known for measuring wind speeds but not so much measuring temperature or latitude/longitude. Standardized tests are used to measure civility, aka the level of a society in this case.

[gamecreator]

Huh, so I failed to translate it.
And doesn't civility means politeness?
And how can you ever measure speed of wind with barometer?

[Davecom3]

Possiblhy another mistranslation or misthought, as I focused more on my thought that baro- in barometer relates to wind, which was in itself a misthought. Probably, it is more "plays a part in the measurement done by".

[Davecom3]

A friend of yours is tossing a coin and you are betting him on the outcome. You bet heads every time. Your unit stake is $1 per toss. You begin by betting $1 on the first toss. If you win, you again place $1 on the second toss but if you lose you double the stake to $2, then $4, and continue to double after every loss. After every win, you revert to the $1 stake. After 200 tosses of the coin, heads has come up 98 times. How much money have you gained/lost, assuming the two-hundredth toss was heads?

[gamecreator]

98$. Strategy guarantees 1$ profit every time heads appears. Since there were no tosses after last heads appeared, there was no loss.

[Davecom3]

Correct.

[gamecreator]

[Loki]

The requested angle is 150 degrees.

[gamecreator]

What's solution?

[Nerre]

Lets us put a L behind those for the left triangle, B for the below triangle and R for those of the right one.

AB and BC appear to have the same length, maybe that is what the = on the line should indicate.
=> Afull and Cfull = (180 - 80)/2 = 50┬░
=> 50 - 10 = 40┬░ for AL and 50-30 = 20┬░ for CR

=> 4 formular:
BL + BR = 80┬░
BR + DR = 160┬░ (180 - CL with CL = 20)
BL + DL = 140┬░ (180 - AL with AL = 40)
DL + DR = 220┬░ (360 - DB with DB = 140)

But those 4 seem not to be linearly independent, since we can create some of them by combining some of them. I cannot solve it without getting one more formular. Anybody got one?

By the way: DR = 150 works with those formulas, but we don't know yet if it is the only solution, and how he got to the 150.
Proof by counterproof: DR = 140 or 130 also solves those formulars.

I am missing one point, but could not find it yet.