Iftach Nachman's Riddles Page
These riddles were originally compiled by Iftach Nachman. He no longer hosts this web page; he has kindly permitted me to host it on his behalf.
Knight, Knave, Spy
You meet 3 people: an absolute truth teller (a knight), an absolute liar (a
knave), and a spy (unpredictably answers truth or lie, however he feels like).
They all know each other. You can ask one person at a time a yes/no question.
Can you tell which is which with 3 questions in total? (NOTE: I know some
questions will yield the answer "don't know" or some other unpredicted answer
when referred to the truth teller or the liar. Let's say they are not legal.
(The solution I know contains no such questions.)
The lazy antenna technician
You are an antenna technician, arriving at a 100 m tall broadcast tower. The
elevator is broken, and there is no one around. There is a bundle of 120
electrical wires going from the top of the tower to its bottom. Both ends of
each wire are exposed and free to manipulate. Your mission is to mark which
wire end at the top corresponds to which wire end at the bottom. You have a
roll of duct tape and a marker pen to do that (by putting on 240 little labels
on the wire ends).
The only other tools you have are a battery connected to light bulb, and 2
sockets enabling to close a circuit.
Of course, you want to do that with the minimum number of ascents/descents in
the long tower staircase. NOTE: This is no McGyver puzzle. The only thing you
need to know is that when you close the circuit by plugging in two ends of a
contiguous wire, the light goes on.
Meeting strangers
(This riddle is also mentioned on my own riddle
page, but I'm leaving it here for the sake of completeness.)
The professor and his wife are having a party. The guests are 4 couples. When the guests arrive, each person shakes hands with the people he/she doesn't know. The professor asks each one how many hands they shook, and gets 9 different answers. How many hands did the professor's wife shake? (NOTE: No missing data here!)
Light bulbs and dwarves
There are a 100 light bulbs on the table. Dwarf no. 1 starts marching along the
bulbs, changing the state of each bulb. (i.e. switch on a bulb that is off,
switch off a bulb that is on). After that, Dwarf no. 2 marches along the
bulbs, changing the state of every second bulb he encounters. Dwarf no. 3
changes the state of every 3'rd bulb, etc. until dwarf no. 100 changes only the
state of the 100th bulb. Assuming all bulbs were off at the beginning, which
bulbs will be on after the 100th dwarf steps off the table?
Squares and kites
Prove/disprove: Can you tile a square with a finite number of
kites? A kite is a quadrangle with one internal angle bigger than 180
degrees. Only very basic geometry needed here. Thanks to Alon Amit.
Leaping frogs
Four frogs are standing on a plane. Each frog can advance by jumping over
another frog, a distance which is double the distance to that frog. (e.g. if
frog A is 3 m away from frog B, it can jump over it a distance of 6m; after the
jump frog A is still 3 m away from B, but from its other side) Prove/disprove:
If the frogs are initially standing on 4 corners of a square, can they reach a
state where they stand on the corners of some larger square? (Thanks to Alon
Amit.)
100 prisoners
(As mentioned by Iftach Nachman himself below, this riddle is also mentioned
on my own riddle page, but I'm leaving it here for the
sake of completeness.)
100 prisoners are locked up in prison. Each prisoner in his own cell. They cannot communicate with each other, except for the one afternoon when they all arrived in prison. Every day, the warden picks one prisoner at random and brings him to a room with a lightbulb and a lightswitch. The lightbulb is in whatever state it was left the day before. The prisoner can now choose from 3 things: 1) he leaves things as it is, 2) he toggles the lightswitch 3) he states that all 100 prisoners have been in this room at least once. After option 1 or 2, the prisoner is brought back to his cell. If the prisoner decided to go for option 3, but he is wrong, they are all executed. If he is right, they all go free. Given that the prisoners are aware of this evil game that the warden is going to play with them, what is the strategy they should decide on the day they arrived in prison, when they could still talk to each other? Assume the prisoners know the bulb is initially at the off position. Note: random means random. It may happen that the same prisoner is chosen 2, 3, or more days in a row. (Thanks to Thomer Gil.)
Other nice riddle pages
Hard interview questions
Thomer M. Gil's riddle page
Rustan Leino's puzzle page