They all said


They all said Horseback: Car: Boat:


I've tried to explain the solution using as little math as possible, and to give some intuition as to what makes it tick. Nonetheless there will be a little mathematical notation at the end. First steps: going beyond the obvious solution in the simplest case (N=2) The statement of the puzzle as presented here doesn't make this very clear, but the puzzle ...


Remove one egg. Now the number of eggs is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10. Therefore it is divisible by their least common multiple. There are algorithms to compute the LCM; for example you can write the prime factor decompositions and take the maximum for each factor. Here the result is 7*5*9*8 = 2520. So the original number of eggs is of the form ...


A dwarf with a red dot will A dwarf with a blue dot will Therefore, on the $N$th day, all dwarves with red dots are present, and all dwarves with blue dots are not.


Such an old chestnut! Each of them eats 5/3 loaves. The first traveler contributes 3 loaves, eats 5/3 himself, and gives 4/3 to the extra traveler. The second traveler contributes 2 loaves, eats 5/3 himself, and gives 1/3 to the extra traveler. Since the first traveler gives 4 times as much bread to the extra guy, he should also receive 4 times as much ...


They all said: Valid if not 100% useful.


Wikipedia has a nice article on this. Buffalo buffalo (buffalo from Buffalo NY) [that] Buffalo buffalo buffalo (that the buffalo from Buffalo NY bully) buffalo Buffalo buffalo (are bullying buffalo from Buffalo NY).


You and Roger are out of luck. Let the side length of the cube be $s$, so there are $s^3$ sodas. If $s$ is odd, then there will be an odd number of sodas left over, since $s^3$ is odd, and removing 4 from an odd number leaves an odd number. If $s$ is even, so that $s=2t$ for some $t$, then there will be $8t^3$ sodas, which is exactly divisible by $4$, so ...


I've seen a variation of this before:


The real data set is: First clue: Second clue:


Another way of getting the same answer as Gamow is to have each traveller notionally pay \$5. That gives them a pot of \$15, from which they distribute the money to those who provided the bread. They have \$3 a loaf, so: - the first traveller pays \$5 and gets \$9, for a total of \$4 - the second pays \$5 and gets \$6, for a total of \$1 - the third just ...


In order to solve this problem, I used a combination of a flood-fill algorithm and Dijkstra's algorithm. I set up a large grid of cells over the map. Each cell remembers its current distance and its "last source." The initial cell (the location of the ship) starts with zero distance, and source equal to itself. All other cells are uninitialized. The ...


I don't have time to flesh out every detail right now, but the story is clearly Some of the clues that give it away: Some more: In the back-story:


The kingdom is guarded from foreigners, therefore the password is based on native language (which is of course English:):) ).


The basic idea is to work backwards. A cute trick is to recognize that there could have been


I would suggest the combination Firstly, the "asking" code combined with the row of numbers suggests that they spelled out a word in ASCII code. The numbers on the front of the safe only go to 100, so Mort was probably using the hexadecimal notation for ASCII, since the decimal notations for standard letters go up to 122. The fact that all the numbers were ...


Assuming a mistake in the problem layout, we could get something with some significance: The error would be And with this


Gilles certainly has the right idea, find the LCM of 2..10, +1. To take it a but further, here's the method I find easiest to find the LCM of relatively low (and/or easy-to-factor) numbers. First, find the prime factors of all the numbers: $$ \begin{array}{c|l} 2 & 2 \\ 3 & 3 \\ 4 & 2, 2 \\ 5 & 5 \\ 6 & 2, 3 \\ 7 & 7 \\ 8 &...


Let's replace the place with New York Let's replace the verb with bully Let's keep the animal as buffalo Original: Buffalo buffalo (that) Buffalo buffalo buffalo (also) buffalo Buffalo buffalo. Replaced: New York buffalo (that) New York buffalo bully (also) bully New York buffalo.


Given that there's little context, it's hard to give a definitive answer, but I'd have to guess that the answer you are looking for is: This can be found by:


He calculated the area using Pick's Theorem. Area = (number of internal grid points) + (half the number of boundary points) - 1 The area is $149 + \frac{21}{2} - 1 = 158.5\mbox{ units}^2$ Since we're given that the units are $50\mbox{ ft}$, the area is $396250\mbox{ ft}^2$.


This one is very literal. Also,


I think the answer is: H C P L


Found it: "It is true for all that that that that that that that refers to is not the same that that that that refers to." Meaning: It is true for all that, that that "that" which that "that" refers to is not the same "that" which that "that" refers to. Or perhaps more clearly: It is true, despite ...


Answer: Explanation:


On the first day Use 10 groups of 2 prisoner and number them 0.0, 0.1, 1.0, 1.1, 2.0, ..., 8.1, 9.0, 9.1. Prisoner a.b drinks from bottles with $\left\lfloor\frac{index}{2^a}\right\rfloor\%2=b$. That means every bottle where the ath bit is b. That gives us some groups where one prisoner survives and some groups where both prisoner survives. Take a random ...

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