Look Ma, I can rhyme... ;P

I get excited by the light,

I jump from state to state,

No one can be exactly like me,

My brothers I do hate,

If when I turn one way you turn the other,

You can be my mate,

You can try to guess what I'll do next,

But I don't believe in fate.

Who am I?

For those of you whom this is obvious, please wait a little while and give others a chance to guess. Thanks!

I got myself into such a state working this out...

Haha, nice.

Okay, so I came up with this as a byproduct of a failed attempt at another puzzle...

Fill in the next two numbers:

111

2024

31

1320

1413

126

1422

315

1518

2325

This requires some outside knowledge...you may have to look some information up (not related to math/numbers), but after getting the first few numbers, it should be pretty obvious what the pattern is and what you need to know/find out

Good luck!

I think I got it...the third one was throwing me off until I thought of n-parity...

I noticed that the decimal values corresponded to 8ths, so I put them all in terms of 8ths, and the values become: -32/8,-31/8,95/8,825/8,16449/8,134098/8

The differences between the numerators are then: 1=1^6, 126, 729=3^6, 15625=5^6, 117649=7^6

So I was confused since the 2nd transition didn't match (2^6=64) until I realized that -(-31)+64=95, and 2 is the only *even* number in the bunch...

So I think the formula should be as below:

a(i) denotes the ith number in the sequence, starting with i=0 (I start at a(0), that is, -4=a(0), -3.875=a(1), etc)

n(i) denotes the ith prime number, counting 1 (so 1,2,3,5,7,11,etc...)

The formula should be a(i)={[(-1)^(n(i)-1)]*[a(i-1)*8]+ n(i)^6}/8

or formatted to be easier to read(I hope i did it right): a_i = {(-1)^(n_i-1)(a_i-1*8)+n_i⁶}/8

The (-1)^(n(i)-1)=1 for all odd n(i), so it only effects the sign of n(i)=2, which solves that issue...

Anyways, I hope all my parentheses are in the right places, but I get that the next number in the sequence = (134098+11^6)/8=1905659/8 =238207.375

Oh, this also works if you use n(i)+1 or n(i)+3 or n(i)-3 or any n(i)+/-2(integer) instead of n(i)-1 as the exponent...the only thing that matters is the even/odd parity

Nice sequence Data! I'm still working on the one in the newest post...

*Cough* *bump*

Gaaah, this is hard...

Here's a question (fishing for a hint I guess ):

Is this sequence self-contained or do you need some piece of outside information (like particular dates or, like, # of something in something else, etc)?

Oh, and I don't know if this means anything, but:

If you add the digits of the first four numbers you get the last half of the next number, i.e. 1+9+2+0=12, 2+0+1+2=5, 1+5=6,1+8+6=15

but after that, the pattern fails, so it may be just a coincidence...

http://www.cut-the-knot.org/Probability/Am....shtml#solution

Oh fine, do it the *easy* way... ;P

Err, my notation was off in my earlier post...sorry, it's been while since I took Probability Theory...

Anyways, hopefully this will make things clearer:

Okay, first off, for those who are unfamiliar with conditional probabilities, here a short explanation:

P(A|B) is the conditional probability of A given B. This means it is the probability that A will occur if B occurs.

P(A) = P(A|B)P(B)+P(A|C)P©+P(A|D)P(D)...

The probability of A is equal to the conditional probability of A given B times the probability of B plus the probability of A given C times the probability of C and so on for all possible events (B,C,D, etc.)

So Bonanova's earlier formula was correct:

P[extinction] = P[ext1] + P[ext2] + ... + P[exti] + .... where P[etxi] is probability of all the amoebae of the ith generation dying.

However, what my point is, and what I think Unreality's point is is that P(exti) is NOT simply equal to (1/4)^2i. (1/4)^2i = P(exti|isurv), that is, the probability of extinction in the ith generation given that all the previous generations have survived, hence, there are 2i amoeba which each now have a 1/4 chance of extinction.

So to get P(exti), we need to take P(exti)=P(exti|2isurv)P(2isurv)+P(exti|2i-1surv)P(2i-1surv)+P(exti|2i-2surv)P(2i-2surv)+...+P(exti|2surv)P(2surv)+P(exti|1surv)P(1surv)

for each i. To get the total probability of extinction, we then need to sum these for all the ith generations from 0 to infinity...

I think it probably simplifies to something nice, which someone may have suggested already, but I'm still working on that...

Okay, hmm...well I had hoped this would clarify the matter, but it may just make things more confusing...but I'm pretty sure the logic is correct.

Oh well, thanks for the puzzle!

You ask the chance of not dying out.

That's 1.00 - P[extinction].

P[extinction] = P[ext₁] + P[ext₂] + ... + P[ext_i] + .... where P[etx_i] is probability of all the amoebae of the i^th generation dying.

P[ext₁] = 1/4. The others are quickly decreasing but positive.

The sum P[ext] is thus kind of but not much larger than .25 -- perhaps .3 or .33.

Thus P[eternal survival] = 1.00 - something between say .25 and .35 = something between .65 and .75

Yeah, I think Unreality is right about it not being a simple 1-(1/4)^n geometric series...the answer should be an infinite series of conditional probabilities.

[spoiler='Conditional Probability

']Like, you can't just sum the P(ext), as you call them, of the ith generations. You need to sum the P(exti)P(survi-1), where P(survi-1) is the probability of survival to the i-1 th generation. Put in less mathematical terms, it means you need to weigh the probability of extinction of that generation with the probability that the amoeba will actually survive to that generation. So it should be something like P(survival to infinity) = 1-sum(P(exti)P(survi-1)), and in the P(survi-1), you need to take into account the different cases where 1 out of 2 survives or both survive...

I haven't done the math yet, but it wouldn't surprise me it that series came out to sum to 2/3 as well...once I have time, I'll try to figure out the exact mathematical exp​ression for the series

Not enough information? Think about it. There is enough information to tell that the conjugate picked him up sometime after 18:00, but before 18:23. However to know how the time splits between his walking travels and his conjugates mode of transportation, you would first need to know their respective speeds. If both were traveling the same speed then I could confidently agree with the above poster, but such is not the case.

No, Starfish is correct (nice job, btw!). You don't need to know speeds. The way I look at this problem is in terms of time-distances (such as light-years), and then all you need are times. Thanks guys!

Thanks to my friend who I stole this from...(oh well, he will never know ;P)

A commutator commutes to his group at work and back to his community locomotive station daily, arriving at 18:23. His conjugate drives from home to pick him up. Like all conjugates, they are very precise, and arrive precisely as the train arrives. One day, the commutator arrives at 16:23 due to an early release day. Since he did not want to interrupt his conjugate's train of thought, he simply started walking home along the route that which they traverse daily. The conjugate pairs meet along the path, and immediately head back home. They arrive home 23 minutes earlier than usual. How many minutes did the commutator walk before he was picked up by his conjugate?

Just my 2c, and not too far away from what someone's already said above.

He was a DJ who had left a tape (do they use those any more??) playing while he nipped out to, let's say, kill his wife.

When the tape jams (file glitches, CD skips etc for the under 40s!) he realises his alibi is blown and chooses to take his own life.

Yeah, that was pretty much the same thing I said, but you said it much more concisely and to the point ;-). Thanks!

Btw...is the person who started the thread checking it?

Yep, basically between all of you, I think you got it...

His reply was "But Duke, you not only ate the watermelon with the rest of us, you ate the rinds as well, so does that not make you the one who is the pig?"

I thought it was clever because while the Duke focuses on the evidence that is there, Afanti focuses on the evidence that is missing, i.e., the missing rinds.

Not yet...but getting closer

Okay, the first thing I did after registering in this forum was to read the Important:READ BEFORE POSTING, and I did do a search, but I know I'm not good at searching for variations, but I don't think this hasn't been posted yet...

Afanti is eating watermelon with the King and some courtiers. Among the courtiers is a Duke who is jealous of Afanti's favor with the King and therefore is constantly trying to embarrass Afanti in front of the king. So after eating his slices of watermelon, the Duke covertly pushed his watermelon rinds in front of Afanti. After they are done eating, the Duke points at Afanti's pile of watermelon rinds (which is twice as large as the other guests' piles) and gleefully proclaims "Look at how much Afanti has eaten. He is such a pig!"

Afanti looks at the Duke and calmly gives his reply. The Duke becomes red-faced and is embarrassed in front of the King. Score another one to Afanti!

What was Afanti's reply?

Okay, this is a totally awesome forum! Here is one of my favorite brain teasers that I got from a friend a couple years ago (and probably the reason I don't like soup...):

A man walks by a restaurant and sees penguin soup on the menu. He goes into the restaurant and orders penguin soup. The waiter brings him the soup, he eats/drinks it, pays the bill and leaves the restaurant. He promptly goes home and shoots himself. Why?

Enjoy! ;P

A guys comes rushing out of his house, gets into his car, turns on his radio and then speeds off in the freeway. On his way, the radio program suddenly stops so he pulls over and shoots himself. Why?

He was a dj or whatever they call those people who host radio shows and he pre-recorded the show he was suppose to do that day in order to give himself an alibi. He was probably at home murdering his wife or something and when the program stopped, he knew his "trick" (as they call them in anime ^_-) and he would be caught and given the death penalty or something, so he shoots himself.

language or memory?

so "twilight" actually refers to when the time of day when the sun is below the horizon, like dawn or dusk, and the sun's light gets refracted by earth's atmosphere to higher wavelengths (more red) so my guess is infrared light (which is just above the visible wavelength range)?