NeoPets Riddles (Lenny Conundrums) and Answers Here

hmmm, goiing with koi..
first dice you need a k, o or i... so thats a chance of 3/6
second you a o or i... so thats a chance of 2/6
last you need a 1.. so thats a chance of 1/6
but nou the other dices.. i don't know what to do with them.. anyone?
or is it 3/6 x 2/6 x 1/6 x 6/6 x 6/6?

There are fewer than 576 ways to get Eyrie.

Suppose you had 5 dice with the letters A, B, C, D, and E and you wanted to get the letters ABCDE in any order. The number of different orders for these 5 letters is 5! or 5*4*3*2*1 = 120.

However, if you want to get AABCD, you no longer have 120 different ways to make that show up. The repeat means that there are 120/2! = 60 orders.

EEYRI and IIKYR each can show up 60 different ways by the same argument.

Kiko and Koi require a different argument. Any time a set of dice can spell Kiko, it also can spell Koi, but there are cases where the dice can spell Koi but not Kiko (ie, RRKOI).

Hey... Can't we use nCr? I remember that probability is

(total possible)/(total)

so (nCr for every possible situation) / 30C5

30 because there are 5 6 sided dice so 30 sides, 5 because we are rolling 5 of the sides.

So, for the easiest one, KOI, it is

(6C1 * 6C1 * 6C1 * 6C3 * 6C3)/ 30C5

I think

Maybe i'm wrong

Just wanna say all of the answers so far have been WAY TOO HIGH!

Think about it, how could it possibly be to roll a KOI with five dice?? have you ever played yahtzee?? think of Koi as a 123 and then think if your rolling three dice how it could possibly be over say, 20:1...

I think ive got the answer (its not 20:1 ), so far the Eyrie and Kyrii math has been correct, but the Koi makes all the difference.

ok... I think i get this!

eyrie= 5/6 * 4/6 * 3/6 * 2/6 *1/6
Kyrii=5/6 * 4/6 * 3/6 * 2/6 *1/6
kiko=4/6 * 3/6 * 2/6 *1/6 * 6/6
koi= 3/6 *2/6 * 1/6 * 5/6* 5/6

I think this, because, witht the kiko koi confuddlement, you cannot have 6/6 for the last 2 dice, incase it's the other k. Therefore, you times by 5/6 not 6/6

So the answer I got was.... 1 in 34.79.........

Rounded to 1 in 35.
Am i correct???

I got a surprisingly low answer. Remember the LC asks for ODDS not probability. Please refer to Lenny Conundrum Round 141 (The Bilge Dice Perfect Game One). Hint: Treat the case KIKO separately then KOI. That, assume you have the word KOI but the other two dice do not show K.

Good Luck!

My calculation:

Number of possible throws: 7776

How many possible ways to spell KYRII:
5 places for the K, 4 places for Y, 3 places for R. The rest must be I and I (1 possibility). Multiplied: 5x4x3x1=60

How many possible ways to spell EYRIE: same as above, 60.

We do not need to worry about KIKO, because that is a subset of all possible throws that allow us to spell KOI.

How many possible ways to spell KOI? That is, K, O, I and 2 arbitrary letters that can be in 5x4 places and can be 6x6 different combinations. The remaining 3 dice have 6 ways to spell KOI, therefore: 6x(5x4)x(6x6)=4320

Summed up, 60+60+4320=4440 possibilities.
Odds would be 4440:(7776-4440) or about 1:0.75, rounded 1:1.
Or if it is 4440 in 7776, it would be about 1 in 1.75, rounded 1 in 2.

What is correct?

edit: messed up on this, the 2 arbitrary letters can be in 5x4 places divided by 2 = 10 :-(

so the correct sum is 120+6x10x36=2280, yielding odds of
2280:(7776-2280) or 1:2.41, rounded 1:2.
2280 in 7776 would be 1:3.41, rounded 1 in 3.

you are close httpd, but I think you need to take another gander at your method for finding KOI.

Now After looking at PinkPT history for LC Round 141, I believe they do want the answer to come from odds, not probability.

You are right. I still counted some dice constellations twice or even three times:
Take XXKOI.

If one of the X is a K, for example the first, I counted the constellation one more time as
KXXOI
with the second X a K.

If both of the X are Ks, i counted it two more times as
KXXOI and XKXOI.

The number of KOIs is actually smaller than 2160, resulting in a higher number in the odds.

It is actually easier to do it as you suggested, but I already submitted a wrong answer. I leave it to the others to find out. Don't want to spoil everybody's fun figuring it out :wink:

Oh, and the difference between odds and probability IS important, no matter how big the numbers are. It is always a difference of exactly 1 in the solution.

I meant to say in my above post, that for neopets LC, the writer does not make a distinction between odds and probability. Maybe it is another one of those British things, although MATH definitions are UNIVERSAL!

NeoPets says they are looking for the ODDS of being able to spell a NeoPet species name.

Maybe I'm being a bit nub. But wouldn't the odds of being able to spell a neopets name be 1 / 1?

Seriously.

If you rolled 5 E's. You could do Eyrie.
If you rolled 5 O's. You could do Bori.
If you rolled 5 I's. You could do Eyrie.
If you rolled 5 Y's. You could do Eyrie.
If you rolled 5 K's. You could do Kacheek.
If you rolled 5 R's. You could do Bori.

Am I missing something? Or is the answer very obvious...

Well, actually I think httpd is damn right..

U guys should check page 493. Everyone says that the answer is 177. Seriously. Check it out. Or else !!! JK.

Alternative solution
Hi ^^
I've reached other solution, and since you guys are 'pro' solvers.. I just want your opinion.
So, here I go:

------------------x

The four pets: EYRIE, KYRII, KIKO, KOI

Odds for EYRIE

5 dies are rolled: _ _ _ _ _
How they must turn up: E Y R I E
1st blank--> must be E--> odds 1/6
2nd blank--> must be Y--> odds 1/6
3rd blank--> must be R--> odds 1/6
4th blank--> must be I--> odds 1/6
5th blank--> must be E--> odds 1/6

Odds for EYRIE: 1/6 * 1/6 * 1/6 * 1/6 * 1/6 = 1/7776

Odds for KYRII, same as odds for EYRIE (see above)

Odds for KIKO

5 dies are rolled: _ _ _ _ _
How they must turn up: ? K I K O (or) K I K O ?

1st alternative, odds:

1st blank can be anything--> 1/1
2nd blank--> must be K--> odds 1/6
3rd blank--> must be I--> odds 1/6
4th blank--> must be K--> odds 1/6
5th blank--> must be O--> odds 1/6
Odds for ?KIKO: 1/1 * 1/6 * 1/6 * 1/6 * 1/6 = 1/1296

2nd alternative

1st blank--> must be K--> odds 1/6
2nd blank--> must be I--> odds 1/6
3rd blank--> must be K--> odds 1/6
4th blank--> must be O--> odds 1/6
5th blank can be anything--> 1/1
Odds for KIKO?: 1/6 * 1/6 * 1/6 * 1/6 * 1/1 = 1/1296

Total odds for KIKO = 1/1296 + 1/1296 = 2/1296

Odds for KOI
5 dies are rolled: _ _ _ _ _
How they must turn up: ? ? K O I (or) ? K O I ? (or) K O I ??

1st alternative, odds:

1st blank can be anything--> 1/1
2nd blank can be anything--> odds 1/1
3rd blank--> must be K--> odds 1/6
4th blank--> must be O--> odds 1/6
5th blank--> must be I--> odds 1/6
Odds for ??KOI: 1/1 * 1/1 * 1/6 * 1/6 * 1/6 = 1/216

2nd alternative, odds:

1st blank can be anything--> 1/1
2nd blank--> must be K--> odds 1/6
3rd blank--> must be O--> odds 1/6
4th blank--> must be I--> odds 1/6
5th blank can be anything--> 1/1
Odds for ?KOI?: 1/1 * 1/6 * 1/6 * 1/6 * 1/1 = 1/216

3rd alternative, odds:

1st blank--> must be K--> odds 1/6
2nd blank--> must be O--> odds 1/6
3rd blank--> must be I--> odds 1/6
4th blank can be anything--> 1/1
5th blank can be anything--> 1/1
Odds for KOI??: 1/6 * 1/6 * 1/6 * 1/1 * 1/1 = 1/216

Total odds for KOI: 1/216 + 1/216 + 1/216 = 3/216

Total odds for EYRIE + KYRII + KIKO + KOI = 1/776 + 1/776 + 2/1296 + 3/216 = 122/7776 = 1/64 (approximate)

-------x

So, what do you guys think?

PS: yes, i have read the previous posts/solutions

secrecy, your solution did not account for the possibility of rolling the letters in different combinations

i.e.
Y for the first blank
E for the second blank
R third
I fourth
E fifth

the letters can still spell out EYRIE, just in a different order.

I get:
kyrii: 60 ways
eyrie: 60 ways
kiko: 260 ways
koi: 970 ways (that don't include kiko)

Assuming I didn't make a mistake, the total is 1350. Therefore, probability is 1350/7776 = 1/5.76.

Odds are usually expressed as something TO something, not something IN something. So, assuming they want probability, 6 would appear to be the answer.

Hmm.. I wasn't a very big fan of the idea rolling 5 dice, getting

I O E E K (ie)

meaning that you are able to spell K O I..
but now.. i think i have it in other perspective...
I'll try to do the math for that one too, although i already submitted my answer.

but i think when spelling KOI, you should count the KOI's in KIKO, too. after all, you are able to spell it. EDIT: No, nevermind that, then i think the answer '6' provided by the user above is right

also, odds, i think neo meant probability, as it is commonly misued, (ie)
someone asks you, what are the odds of getting 1 when rolling a die?
you answers 1 in 6, not 1 to 5, right?

anyways, i think if you answer odds or probability, neo will see that they mixed up a little in math terms and they might consider both answers.