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# Pickett

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## Posts posted by Pickett

1. ### Did you get more than me?

Spoiler

B and C each have 1 piece...D has X pieces (where X>1), and A has 11-X pieces.

Let's walk through this:

We are starting with the assumption that everyone got at least one piece

When A asked B if he had more and B said "no", the only way he could know that is if B only received one piece...Because with that, there is no way he could've had more than A...he could have had the SAME, but not MORE.

So then B asked C the same, and the same logic applies. So B and C each had 1 piece.

At this point we know B and C each had 1 piece, which means there are 11 pieces unaccounted for. D knows all of this information because of what he just heard, and as long as he has 2 or more, he knows he has more than C...and he would know exactly how many because A would have (11-D), which is why he can say his statement.

If our original assumption is incorrect, and people were allowed to have 0, then B and C both had 0 as CaptainEd mentioned...although D would have at least 1, not 0, and A would have the rest.

2. ### Submitted for your perusal

This is either sheer madness or complete brilliance.

It's a lot to read, and I've only briefly skimmed it because i don't know if I have that much time to dedicate to it, but I've definitely noticed a number things out of this that will start to relate each of the paragraphs and "poems" together as well as a number of random pieces of information. A few examples I found:

• It ends with an Irish Blessing (although it is missing the final piece: "May God hold you in the palm of His hand.")
• There is an entire section containing pieces of song lyrics (Lou Reed - Walk on the Wild Side, Leonard Cohen - The Future, Simon and Garfunkle - The sound of Silence, Schoolhouse Rock - Conjunction Junction, The Trashmen - Surfin Bird, Gorillaz - Empire Antz, Tom Petty and the Heartbreakers - Runnin' Down the Dream, etc)
• There are repeated phrases or words that seem too coincidental across the paragraphs ("Four Seconds", "Military Bases", "Capital G God", etc)

So, again, I'm not going to have time to spend digging into this, and i'm still not completely sure if it's actually worthwhile, but it definitely piques my interest and will be checking in on this one...

3. ### Thinking of a Number

Mind telling us (or PMing me) the answer? as it has been 6 months with no correct answers and the participation seems to have dwindled...

4. ### Emoji based math puzzle - level easy!

Spoiler

These emoji math things are always the same...

By equation 1: wink = 10
By equation 2: devil = 5
By equation 3: hearts = 7

Now, with equation 4, you do have to make an assumption that the smiley behind the first winking is a second winking (likewise with the heart smiley) AND that the expectation of having 2 of them together means addition...but assuming those things, you have what Kapris said:

(2*7)+5*(2*10)

...but the ANSWER to that is not 380, it is 114.

5. ### Crystal Problem

Spoiler

Isn't it just the tetrahedral numbers...the formula for the series is

Sn = n(n+1)(n+2) / 6

So, for n=1,000,000, you have ((1,000,000)(1,000,001)(1,000,002)) / 6 = 1,000,003,000,002,000,000 / 6 = 166,667,166,667,000,000

6. ### Crystal Problem

Spoiler

166,667,166,667,000,000

7. ### Chess Knight Problem

Spoiler

My first stab at it I got 12 squares.

0,0
1,2
2,0
3,2
1,3
2,1
0,2
1,0
2,2
3,0
1,1
0,3

8. ### Bisecting a triangle

I'll take a quick stab at it:

Spoiler

sqrt(2π) / 4 = ~0.62666

The "obvious" first answer is sqrt(2) / 2 (bisect the 90 degree angle perpendicular to the hypotenuse)...But if we step back and look at it a different way: The current triangle has an area of 1/2...

So, we simply need to make a cut that leaves two areas of 1/4 (not necessarily similar shapes). The shortest STRAIGHT cut would be the sqrt(2) / 2, but if we decide to make a curved cut, we can get it shorter. I'll try to describe it (can't add pictures right now)

Choose one of the 45 degree angle points and center a circle there with radius r. Mark the points along the hypotenuse and adjacent leg at points to create a segment of a circle with a 45 degree angle and radius r. We know, then, that is exactly 1/8 of the area of the full circle. Since we are trying to get an area of 1/4, and we have 1/8 of a circle, the full area of the circle would be 2. so we can figure out the length of r by doing πr2=2. Leaving us with r = sqrt(2π) / π

Given that, we need to find the length of just that arc of the circle...which is 1/8 of the perimeter. So we know P=πd...which leaves us with P=2*sqrt(2π). Divide it by 8, and you get sqrt(2π) / 4 as the length of the arc connecting your points...leaving 2 pieces of the triangle with areas of 1/4 each.

9. ### Binary lock

Spoiler

Worst possible number of moves: 2n - 1

I'm still working on formalizing the pattern to follow...in my head it's almost similar to the Towers of Hanoi (but using binary)...but trying to figure it out how to describe it...

10. ### Thinking of a Number

5 hours ago, Biotop said:

The number I am thinking  of is specific, one word and familiar to everyone.

Well then I've got nothing...closest I can think of that even relates to numbers is

Spoiler

solitaire

11. ### Thinking of a Number

curious as to how obscure these are or even the pronunciation allowed for these. Here are some examples of what I would consider "valid", but probably not what you're looking for:

Spoiler

π/1 = "pi over one"

1.1 = "one dot one"

0.0 = "oh point oh"

So it really comes down to what "words" or "interpretations" are allowed here? Are greek letters allowed? are "non-standard" pronunciations of digits allowed? What about mathematical symbols?

12. ### Celebrity Interview

Spoiler

I'll go with "To be, or not to be..."

Write it as a logical expression (in hex): 2B | !2B

2B = 00101011... !2B = 11010100

So 00101011 | 11010100 = 11111111 = FF

Not sure if that's what you were going for, but it makes sense...

13. ### Thinking of a Number

Spoiler

If you count "y" (which in this case is a vowel): eighty-one

But you didn't have "y" listed, so I'm guessing not...

Spoiler

If you count "y" (which in this case is a vowel): eighty-one

But you didn't have "y" listed, so I'm guessing not...

Spoiler

If you count "y" (which in this case is a vowel): eighty-one

But you didn't have "y" listed, so I'm guessing not...

14. ### Thinking of a Number

Spoiler

If you count "y" (which in this case is a vowel): eighty-one

But you didn't have "y" listed, so I'm guessing not...

15. ### Thinking of a Number

1 hour ago, Pickett said:

not it, I know...but it was close

Hide contents

googolplex

5 vowels, but 10 letters long

Not sure what I was thinking when i wrote that...not even 5 vowels...I'll shut up now ;c)

16. ### Thinking of a Number

not it, I know...but it was close

Spoiler

googolplex

5 vowels, but 10 letters long

17. ### Dots, not hats...

So bonanova's most recent puzzle, Another hat problem, reminds me of one of my favorite riddles that my dad always told me. It's very similar, but slightly different, and I don't think I've posted it before, so here it goes (he was a much better story teller than I, so pardon my narrative):

A king put out a decree saying he will give his entire kingdom to the person who could solve all of his riddles, thereby proving to be the smartest person in the land. Obviously many showed up, but after all of the trials, only 3 people remained. The king told them to get some rest for tomorrow they would face their final challenge. Only one person would remain after it, the other two would be killed. That threat didn't dissuade them, and they all went to bed.

When they woke up, they found themselves all in a room together. Any and all reflective surfaces were covered, and there were armed guards surrounding them. Before any of them could speak, the king told them their challenge:

"While you were sleeping, we painted either a red dot or a blue dot on each of your foreheads. You are not allowed to speak or communicate with each other in any way shape or form. Anyone who does so will be killed immediately. Now, raise your hand if you see a blue dot on someone else's head."

The three people looked at each other and all three raised their hands.

"Good. Keep your hands raised. You may only lower your hand when you can tell me what color dot is on your own forehead. If you lower your hand and do not answer, you will be killed. if you answer incorrectly, you will be killed. If you answer correctly, you will gain all of my wealth, and the other two will be killed. Good luck."

The three looked at each other...what seemed like hours went by with no one answering. You could see they were all straining themselves, trying to figure out how they could know what color dot they had. Their arms started getting tired...

Finally, one of the men got a big smirk on his face. He did some final double checking of his logic and slowly lowered his hand.

"The spot on my head is ... "

Given that the man successfully answered the question, and it clearly wasn't a "guess", what color dot was on his head, and how did he know?

18. ### Another hat problem

Spoiler

Long story short: Adam must have a red hat on.

Let's start from Charlie's point of view:

• If Adam and Bill both had the blue hats, then Charlie would IMMEDIATELY say "RED!" (since there are only 2 blue available).
• If he does yell red immediately, then both Adam and Bill would know their hats are blue.
• Because the OP says that only Adam knew the color, this scenario can be dismissed.
• This means Charlie sees either one red/one blue hat or two red hats and therefore can't know what color his hat is.

Now we move to Bill:

• Because Charlie doesn't respond right away with "red", that tells Bill he and Adam couldn't both have blue hats.
• So if Bill sees a blue hat on Adam, Bill would immediately say "red"...
• If this happens, Adam should know based on the logic above that he has a blue hat on, and so he would say it
• This would mean both Adam and Bill know their color, so this scenario is out as well.
• So that means Bill must see a Red hat on Adam.

So based on the above reasoning, the fact that both Charlie and Bill don't "know" the color of their hats immediately, tells Adam that he MUST have a RED hat on...otherwise, at least one other person would know what color they have.

19. ### Celebrity Interview

Spoiler

I mean, I'll go with the obvious answer that he's interviewing Bill Gates?

20. ### Integer equation?

Spoiler

x3 - y3 factors into (x - y)(x2 + xy + y2)

Which means if there are any integer solutions, x - y would be an integer and be a factor of 217. There are only 4 factors of 217: 1, 7, 31, 217. We also know that x3 > y3, which means x > y. With that information, we can take a "brute force" method to find all possibilities, knowing that x - y must equal either 1, 7, 31, or 217. It would be something like this:

Assume x - y = 1

1. Solve for x: x = y + 1
2. Substitute: 217 = (y + 1 - y)((y + 1)2 + (y + 1)y + y2) = 3y2 + 3y + 1
3. Simplify: 216 = 3y2 + 3y...72 = y(y + 1)
4. Solve for y: y=8 or y=-9
5. Substitute and solve for x to find 2 solutions:
x=9, y=8
x=-8, y=-9

Now just repeat for x - y = 7, 31, 217 to find all solutions (note: after going through this, I realized you could probably logically drop 31 and 217 from the list of possible values from the start)...but regardless, the remaining integer solutions are:
x=1, y=-6
x=6, y=-1

Spoiler

I'd try sending an email to either kobilovingheart@gmail.com or lanelovingheart@gmail.com

Good luck.

22. ### Celebrity Interview

uhhh?

Spoiler

Not really sure what to be solving here...but maybe

11111111 (or 255)...since FF is hexadecimal, and the bit-wise representation (hence the "...a few bits of it...") is 11111111?

23. ### ENLIST + SILENT + LISTEN = ANAGRAM

Spoiler

547809 + 087549 + 780954 = 1416312

A=1, E=5, G=6, I=8, L=7, M=2, N=4, R=3, S=0, T=9

24. ### alphametic puzzle

Spoiler

A=1 C=2 E=4 L=9 O=7 P=3 R=8 S=0 T=6

2104 + 2730 + 29704 + 278304 + 279918 + 249918 = 842678

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