Puzzles on dlow's blog

Panza's paradox

Sat, 13 Apr 2019 18:58:12 +0100

Part 1

I have three prizes, and I promise that I will give you either A or B if you give me a true statement and give you C if you make me a false statement.

Q: What statement should you make if you want to get prize A

Part 2

Now I bring in prize D and make you a promise that I will give you either A or B if you give me a true statement and give you C or D if you give me a false statement.

October curiosities

Thu, 12 Oct 2017 00:44:06 +0000

These are some of the puzzles/tricks I’ve been thinking about these weeks.

Dividing area up

You have a 1x1 unit square area that you want to divide into 3 equal area. What’s the least length of lines needed to do so?

Source

Before we try something, we should have a naive solution. We can simply draw two lines. So our answer should be <= 2.

Next, what if we draw a horizontal line that cuts off 1/3 of the area, and then have another line perpendicular to it to divide the remaining area into two. The result there is 1 + 2/3.

An IOI practice round question

Thu, 31 Aug 2017 23:46:47 +0000

There are three people, A, B and C, a 8x8 board with cells labelled 1 to 64, and 64 coins. A and C first goes into a room out of B’s sight. A places a coin on each of the 64 cells on the board. C can flip any number of coins as she pleases and when she is done, she points to one cell on the board. A then flips exactly one coin and C then takes the board out of the room and show it to B. B takes a look at the board, and points to a cell which C originally pointed out in A’s presence. The puzzle is to figure out how that is done.

Nelson Goodman's method

Wed, 28 Jun 2017 00:37:45 +0100

“I am not a liar.” - Everbody

Part 1

There are three brothers: John, James and William. One day you meet one of them on the street and you want to know which of the brothers he is. You are allowed to ask him one question answerable by yes or no.

John and James always lie. William always tells the truth. You wish to find out whether is he John.
Now John and James always tell the truth, and William always lie. You wish to find out whether he is John.

Part 2

There are now only two brothers. One of them is called Arthur. One of them always lie and the other always tells the truth. One day you meet the two brothers together. You are allowed to ask one of them one question answerable by yes or no.

Solving puzzles via programming

Sat, 03 Jun 2017 13:14:45 +0100

Recreational puzzles require only elementary knowledge. It should be easy to understand and it shouldn’t be trivial to solve. Sometimes these problems can be solved analytically. This short entry is about how might computers help us.

Puzzle 1

The string a1 ^ a2 ^ a3 is ambiguous because it could mean (a1 ^ a2) ^ a3 or a1 ^ (a2 ^ a3). There are two different formulas from that string. How many different formulas can the string a1 ^ a2 ^ … ^ an produce?