Tasty Treats from the Moscow Puzzles

“Problems stressing deduction rather than calculation have a special appeal and value. They teach you to analyze, and to seek unorthodox ways of solving a problem.”

—Boris Kordemsky

Today I’m sharing a few treats from The Moscow Puzzles by Boris Kordemsky, which mixes classic brainteasers and original stumpers.

Recreational math expert Martin Gardner called Kordemsky’s book “the outstanding puzzle collection in the history of Russian mathematics.”

Have fun playing logic with your kids!

A Weather Forecast

It is raining at midnight—will we have sunny weather in 72 hours?

Shoes and Socks

I went to the closet while my sister was asleep, so I left the light off.

I found my shoes and socks, but I must confess they were in no kind of order—just a jumbled pile of 6 shoes of three brands, and a heap of 24 socks, black and brown.

How many shoes and socks did I have to take with me to be sure I had a pair of matching shoes and a pair of matching socks?

Apples

Three kinds of apples are mixed in a box. How many apples must you take to be sure of at least 2 apples of one kind? At least 3 apples of one kind?

Arbor Day

On Arbor Day the Young Pioneers of the fourth grade started early and planted 5 trees before the sixth-graders came. But they planted them on the side assigned to the sixth grade.

The fourth-graders had to cross the street and start over, so the sixth-graders finished first. To pay their debt, they crossed the street and planted 5 trees. They planted 5 more trees, and all the work was finished.

Were the sixth-graders ahead by 5 or 10 trees?

[Both rows of trees were the same length.]

A Purchase

“Your pencils, notebooks, and colored paper cost $1.70.”

“I bought 2 pencils at 2 cents each and 5 pencils at 4 cents each—and 8 notebooks and 12 sheets of colored paper, I don’t remember the prices. But the bill can’t be $1.70.”

Why not?

A Crime Story

An elementary school teacher in New York State had her purse stolen. The thief had to be Lillian, Judy, David, Theo, or Margaret.

When questioned, each child made three statements:

Lillian:

(1) I didn’t take the purse.

(2) I have never in my life stolen anything.

(3) Theo did it.

Judy:

(4) I didn’t take the purse.

(5) My daddy is rich enough, and I have a purse of my own.

(6) Margaret knows who did it.

David:

(7) I didn’t take the purse.

(8) I didn’t know Margaret before I enrolled in this school.

(9) Theo did it.

Theo:

(10) I am not guilty.

(11) Margaret did it.

(12) Lillian is lying when she says I stole the purse.

Margaret:

(13) I didn’t take the teacher’s purse.

(14) Judy is guilty.

(15) David can vouch for me because he knows me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?