Logic & Reasoning – Middle Level Problems
Prompt: A certain family party consisted of 1 grandmother, 1 grandfather, 2 fathers, 2
mothers, 4 children, 3 grandchildren, 1 brother, 2 sisters, 2 sons, 2 daughters, 1 fatherin-law, 1 mother-in-law, and 1 daughter-in-law. A total of 23 people, you might think –
but no; only 7 people were present. Can you show how this statement might be true?
Answer: responses vary
Mathematics Teacher March 1992 V85 N3
Brainteasers and Mindbenders by Ben Hamilton (Englewood Cliffs, N.J.: Prentice Hall, 1981)
Prompt: David is a new babysitter for the twins, Michael and Gavriel. One of them
always tells the truth; the other always lies. David doesn’t know which twin is which.
He hears a crash. Going into the other room, he finds Michael and Gavriel standing
around a broken vase. How can David determine which twin broke the vase by asking
exactly one question?
Answer: answers vary
Mathematics Teacher December 1992 V85 N9
Prompt: During a recent span of time, eleven days had some rain. A morning rain was
always followed by a clear afternoon, and an afternoon rain was always preceded by a
clear morning. In all, nine mornings and twelve afternoons were clear. How many days
had no rain at all?
Answer: 5 days
Mathematics Teacher April 2000 V93 N4
Prompt: An over-tired jailer in charge of prison cells 1 through n, goes down the row
unlocking every cell. Then he goes back down the row re-locking the even-numbered
cells. Then he goes back down the row turning the locks of cells {3, 6, 9, ...,}, locking
each one that is unlocked and unlocking each one that is locked. Then he goes back
down turning the locks of cells {4,8,12,...,}, locking each one that is unlocked and
unlocking each one that is locked, etc. After he has done this n times, he goes to bed.
In the morning, the prisoners wake up, and the lucky ones who find their cells unlocked
escape. Who are the lucky ones?
Colorado State University, Math Challenge Website, 2005
Prompt: The Beatles have a concert that starts in 17 minutes, and they must all cross
a rickety bridge to get from where they are to the concert. All four men begin on the
same side of the bridge. You must help them to get to the other side. It is night, and
there is one flashlight. A maximum of two people can cross at one time. Any party who
crosses, either one or two men, must have the flashlight with them at all times during
the crossing. The flashlight must be walked bask and forth, it cannot be tossed, thrown,
etc. Each band member walks at a different speed. A pair must walk together at the rate
of the slower man's pace.
John: 1 minute to cross
Paul: 2 minutes to cross
George: 5 minutes to cross
Ringo: 10 minutes to cross
Example: If Paul and Ringo cross at the same time, a total of 10 minutes will have
elapsed by the time they get to the other side. If Ringo walks back with the flashlight,
another 10 minutes will have passed, for a total of 20 minutes, and you will have failed
your mission.
Source unknown.