[Clank]

1 2 3 4 5 6 7 8
k s t k s t k s there is no room for the last t

[MasterM]

If you need help with more teasers let me know MasterM - I know hundreds.

Sure! I don't know a ton myself and have had to pull a lot of these off of websites, so any help is appreciated

[MasterM]

This one involved some verbal trickery, and was confusing at first. The answer is inkstand. It has kst in the middle, IN the BEGINNING (in is the beginning of the word), AND at the END (and is the end of the word). Pretty clever eh?

Alright so jawfin sent me several puzzles, but I'm going to hold off on using them because I have one that I think is really good. So here goes.

Say there's a reeeeeeeeeally long corridor with a bunch of lights on the ceiling. The lights are operated by pull cords, so you pull the cord and the light goes on or off.

This is a long corridor, remember, so there are 20,000 (twenty thousand) lights.

The lights are all off. Someone comes along and pulls all the cords so that every light is on. Then, someone comes along and pulls every other cord, turning off lights 2,4,6 etc. Then, someone pulls every third cord, and so on, until someone pulls every 20,000th cord. It doesn't matter if the light is on or off when the person comes through, every cord that they're number comes up on is pulled.

So the question is, which lights are on after person number 20,000 pulls every 20,000th cord?

[Cubin55]

I am tempted to make a program just to figure this out, but I will hold off and think this out.

[dent]

Basically what I did was map out the first 20 lights or so manually, and found a pattern. All the lights were off except for 1, 4, 9, 16. (I assumed that everyone left the first light alone since the "every other" guy skipped it) Which means that each light on skipped 3, then 5, then 7, then 9 and so on.

So if you wanted to find out every light that was on you could just plug it into this equation. An+1 = An + 2n + 1 when A1 = 1 until the numbers you got were bigger than 20000. (note An is A sub n, cant write subscript on the forums though i dont think so i just made the font smaller)

This might not be the best way to do this since this pattern might not continue like I said and also would take a little while to work it all out. But I had fun doing it anyways, I haven't done that type of math in awhile lol.

[Fazz]

square numbers are turned on, the rest are turned off then dent?

[dent]

square numbers are turned on, the rest are turned off then dent?

lol yep it would appear that way, didn't notice they were all square numbers

[jawfin]

I'd like to see the code of that program

*spoiler*

The first light is on, and will always stay on as it cannot be reached again.
The second is off and will stay thusly. The way the step over pattern works will eventually light up only the squares. There are 141 squares from 1 to 20000.
I'm sure there must a clean math solution to this, but I can't think of it.

Though I note after posting this others don't bother with a spoiler >.<

[Cubin55]

The code would be in C++ and I just don't want to right now. I think all the numbers that can be squared along the way ore the only ones on.

[jawfin]

I dare say it would be normal C code as any of the extended ++ language would not be required. Here it is in Java, took 5 minutes, but only because I'm a slow typer

Code: Select all

import java.util.*;

public class Lights {

	public static final int LIGHT_COUNT = 20000;

	public static void main(String[] args) {
		Boolean[] mLights = new Boolean[LIGHT_COUNT+1];
		for (int i=1;i<=LIGHT_COUNT;i++)
			mLights[i] = false;
		
		for (int mCounter = 1; mCounter<=LIGHT_COUNT; mCounter++)
			for (int i = mCounter; i<=LIGHT_COUNT; i+=mCounter)
				mLights[i] = !mLights[i]; //this loop is the whole brains
		
		int _lights_on = 0;
		for (int i=1;i<=LIGHT_COUNT;i++)
			if (mLights[i])
				_lights_on++;
		System.out.println(_lights_on+" of "+LIGHT_COUNT+" lights are on.");
	}
	
}

[MasterM]

Dent and fazz were right on, all the perfect squares are on, while all the other numbers are off. The reason being that all prefect squares have an odd number of factors, so the light went from on to off to on, or however many factors.

Next puzzle, this is one of jawfin's

You're doing a crossword puzzle, and come across a clue for a 5 letter word which reads "ABCDEFGPQRSTUVWXYZ". What is the word?

[jawfin]

*Puts hand up* "Sir, I know this one!"

[MasterM]

Dr. Barton! Sit down!

http://m.youtube.com/index?desktop_uri= ... KUmM-7ZnMw

[Fazz]

chemitry lol

'answer' below


i dont have any idea what the word is. But H-O is missing, (H2O - ie water), so its gunna be a 5 letter word meaning along the same lines as dehydrated

[jawfin]

As it's a crossword puzzle, that's the kind of clue one would expect to see - so your answer is right - view it as a "fill in the gap" as opposed to an antonym.

[Fazz]

so it would be htwoo?



Edit: Jawfin edit post to fix spoiler color!

[jawfin]

What I meant is it being a crossword means you'd fill in the bit that was missing, in this case the missing bit is as you said originally being water.

[MasterM]

If you didn't read any of the spoilers flying around out there, the answer is water. The letters h-o (H2O) are missing.

This next one is kind of easy.

A landscaper comes home from work and is talking to his kids. They ask what he did that day, and he says "I planted a lot of trees. In fact, i planted 5 rows of 4 trees."

His daughter, who has just learned her multiplication table, says "oh, that means you planted 20 trees!"

The landscaper says, "No, actually, I only planted 10 trees today."

The question is, how is this possible?

Also, a hint: think outside the box

[jawfin]

A clarification, which is also a spoiler as well as an answer: -

Rows mean parallel lines, but what you suggest indicates they are not.
And yet, 10 trees in one row could be considered as 7 rows of 4: -
1. 1 to 4
2. 2 to 5
3. 3 to 6
4. 4 to 7
5. 5 to 8
6. 6 to 9
10. 7 to 10

So by my method I found 7 rows of 4.

[Fazz]

i like the hint :p

.
...............*
.....*....*......*.....*
.........*..........*
...............*
.......*.............*

i think you can see what im getting at

or my spaces can vanish when i click post :S

hint was kinda a give away, wish i didnt read it before i thought about it :s

[MasterM]

Yup, fazz said it, the hint was a give away, and he plants a star of trees essentially, so that there are 5 rows of 4 trees, but only 10 trees total.

Also sorry I'm not posting every day, I've just been really busy, and am about to go out of town for thanksgiving.

Next puzzle, this is one of jawfin's

On a regular 8x8 chessboard, is it possible to take 31 dominoes and cover each square leaving one pair of opposite diagonal squares open? ex a1 and h8, or a8 and h1. Each domino covers 2 adjacent squares.

[Fazz]

No. By the nature of a chess board, a domino will always cover one white square, and one black square, leaving two oposite squares blank, would mean two of the same colour squares blank. You can leave two lots of two oposite blank spaces, or a1 and h8 free (or any two other random squares), but from this question, i answer no

[Fazz]

since mm hasnt posted, i will post one :p

William lives in a street with house-numbers 8 up to 100. Lisa wants to know at which number William lives.

She asks him: "Is your number larger than 50?"
William answers, but lies.

Upon this, Lisa asks: "Is your number a multiple of 4?"
William answers, but lies again.

Then Lisa asks: "Is your number a square?"
William answers truthfully.

Upon this, Lisa says: "I know your number if you tell me whether the first digit is a 3."

William answers, but now we don't know whether he lies or speaks the truth.

Thereupon, Lisa says at which number she thinks William lives, but (of course) she is wrong.

The Question: What is Williams real house-number?

[jawfin]

*Spoiler*
We are assuming Lisa is intelligent and therefore asking smart questions, only comes to the wrong conclusion due to his lies.

Question 1. We know W told L No, so it must be Yes. (We know or else Q4 would be futile, asking if its in the 30's).

Question 2. W must of said Yes or else L would not of asked Q4 based on her answer from Q3. Casting ahead from Q3 we know it'll be either 9, 16, 25, 36 & 49 (from L point of view). As she asked Q4 we know W said yes here.

Question 3. Yes its a square or else L could not solve it with one more question.

Question 4. L is now thinking of either 16 or 36. We know its neither.

So, a square > 50 not divisible by 4. Can only be 81.

This reminds me of an extremely evil math puzzle of a similar vein - it *is* hard. I'll post it whenever there's a gap for it!

[MasterM]

nice puzzle fazz jawfy, feel free to post yours, since i wont be on much at all to post until next week. (comp is finally fixed btw, but havent installed any steam games yet, so i wont be back on jka for a bit) anyone who was wondering the answer to the chess/dominos puzzle, its no, since each domino has to cover 1 square of each color, and the opposite diagonal sides are the same color, leaving the balance uneven.