1. Page 1 of 4
Navajo Nation Math Circles
http://navajomath.wordpress.com/
20Q
based on Yes and No by Natasha Rozhkovskaya
Here is a map of questions with “yes” and “no” answers. Below it are some animals who
live in the houses on this map. For each animal, follow the questions, starting from the first
one to find out who lives in each house.
1. Is it a wild
animal?
2. Does it eat
fish?
2. Can it live
in an
apartment?
3. Can it
climb trees?
3. Does it
sleep over
winter?
3. Does it
have horns?
3. Does it
bark?
YES NO
YES
NO
YES
NO
YES
NO
NO
YES
YES
YES
NO
NO
A
B
C
D
E
F
G
H
2. Page 2 of 4
Navajo Nation Math Circles
http://navajomath.wordpress.com/
20Q Part B
based on Yes and No by Natasha Rozhkovskaya
Here is a map of missing questions with “yes” and “no” answers. Each endpoint shows a
kind of produce. Supply the questions that would result in the correct identification of the
fruit.
1.
2y.
2n.
3yn.
3yy.
3nn.
3ny.
YES NO
YES
NO
YES
NO
YES
NO
NO
YES
YES
YES
NO
NO
3. Page 3 of 4
Navajo Nation Math Circles
http://navajomath.wordpress.com/
20Q part C
based on Yes and No by Natasha Rozhkovskaya
Next to each house, write the name of a member of one of the members of your family and
then make a series of yes/no questions that would correctly identify them. Ask a group
member to pick one of your family and play Yes/No.
1.
2y.
2n.
3yn.
3yy.
3nn.
3ny.
YES NO
YES
NO
YES
NO
YES
NO
NO
YES
YES
YES
NO
NO
A
B
C
D
E
F
G
H
4. Page 4 of 4
Navajo Nation Math Circles
http://navajomath.wordpress.com/
20Q part D
based on Yes and No by Natasha Rozhkovskaya
D1. I have a few marbles in my pocket (at least one and no more than eight). I can answer
questions only “yes” or “no.” Can you guess the number of marbles in my pocket by
asking only three questions?
D2. Instead of marbles, suppose that I asked the world’s only average two year-old to think
of any word. I would ask YNQs to guess the word. This average two year-old only knows
25 words. How many questions would I have to ask to correctly determine the word?
D3. Repeat the question above for the average:
First-grader: 1000 words
Adult: 6000 words
English professor: 15,000 words
Shakespeare: 60,000
English Language: 250,000 words
D4. The game 20Q should then be able to distinguish between how many objects using
only YNQs?
