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 ...
The solution I read when I heard about this problem (which is most likely the same one in your solution booklet) goes like this:
Before they begin, give each prisoner a fixed number from 1 to 100, and correlate this with their name.
Then, when it is a prisoner's turn to open the boxes, he will start with the box of his own number. If the box does not ...
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 ...
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 ...
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 ...
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 ...
The answer is slightly trickier than you might think at first - it has to do with a quirk in the calendar we currently use, the Gregorian Calendar.
The Gregorian Calendar was instated by Pope Gregory (hence the name) in 1582 to account for a slight disparity in the Julian calendar that made the days drift about 18.75 hours every century. The Julian Calendar ...
We can see that as long as all the countries fire, at least two countries will be targeted. There are eight possible strategies to be played in the first round:
A C G USA CHN GER
C A A 93% 60% 0%
C A C 30% 96% 0%
C G A 90% 60% 30%
C G C 0% 96% 30%
G A A 93% 0% 60%
G A C 30% 90% 60%
G G A 90% 0% 72%
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.
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 ...
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:
2 & 2 \\
3 & 3 \\
4 & 2, 2 \\
5 & 5 \\
6 & 2, 3 \\
7 & 7 \\
Is that tent Good Rice or Bad Rice?
Now look, is that tree over there, is it Good Rice or Bad Rice?
Is this riddle Good Rice or Bad Rice? ;)
Otherwise, it's bad rice:
What about that rock over there? Good Rice or Bad Rice?
Campfire. Good Rice or Bad Rice?
Also, what about this comment? Good Rice or Bad Rice? Bad Rice of course
Let's replace the place with New York
Let's replace the verb with bully
Let's keep the animal as buffalo
Buffalo buffalo (that) Buffalo buffalo buffalo (also) buffalo Buffalo buffalo.
New York buffalo (that) New York buffalo bully (also) bully New York buffalo.
The answer is:
There's quite a walk ahead of you, so you'll need to take a number of steps.
When you're almost there, just let them be the key to unlock the door.
If you take the numbers and:
Then if you use:
You receive the answer mentioned, above.