Problems 1 - 10

1) How Old Are Mary's Kids?

Tom is from the census bureau and greets Mary at her door. The have the following conversation:

Tom: I need to know how old your three kids are.
Mary: The product of their ages is 36.
Tom: I still don't know their ages.
Mary: The sum of their ages is the same as my house number.
Tom: I still don't know their ages.
Mary: The younger two are twins.
Tom: Now I know their ages! Thanks!

How old are Mary's kids and what is Mary's house number? (Yes, there is enough information here to solve the problem!)




2) The Woman With Two Children

This is one of my all-time favorites:

Census Taker: How many children do you have?
Woman: Two.
Census Taker: And their ages?
Woman: One is five, one is two.
Census Taker: Is one of them a girl?
Woman: Yes.

What is the probability that her other child is a girl? (Assume every pregnancy has a 50/50 chance to be a boy or a girl.)




3) The Path to Freedom

Kyle, Neal, and Grant find themselves trapped in a dark and cold dungeon.  (HOW they arrived there is another story.)  After a quick search the boys find three doors, the first one red, the second one blue, and the third one green.

Behind one of the doors is a path to freedom.  Behind the other two doors, however, is an evil fire-breathing dragon.  Opening a door to the dragon means almost certain death.

Given the fact that at LEAST ONE of the three statements on the three doors is true and at LEAST ONE of them is false, which door would lead the boys to safety?




4) Who Had What For Lunch?

Grant, Neal, and Kyle just finished their lunch. One of the boys had a ham sandwich, another a turkey sandwich and the third, a chicken sandwich. If only one of the following four statements is true, who had what for lunch?

  • Kyle had the turkey.
  • Kyle did not have the chicken.
  • Neal did not have the chicken.
  • Neal did not have the ham.




5) The Five Pens

A computer nerd likes to keep five pens in his shirt pocket. The pens are of five different colors and their caps, seen below, are of the same five colors but not a single cap is correctly situated on its colored pen! Given the visible arrangement below and the following clues, can you determine the order of each colored pen?


  • The black pen is next to the pen with the blue cap.

  • The green pen is two pens away from the black pen.

  • The red and blue pens are not adjacent.

  • The yellow pen is second from the left.




6) The Jelly Bean Hunt

Fast Eddie and Slow Sidney were involved in a jelly bean hunt on Easter Sunday. Between the two of them, they found all 15 jelly beans pictured below. With the information given can you determine who found the solid black jelly bean?

Fast Eddie found the pink-striped (#15) jelly bean.

Slow Sidney found a total of five jelly beans; two were striped, one was the solid red one and none were blue (2 and 10) or purple (4 and 12).

The sum of the face value of Fast Eddie's jelly beans totaled 75.




7) The Three Playing Cards

There are three playing cards face-up on the table.

  • A diamond is to the left of a spade
  • An eight is to the right of a king
  • A ten is to the left of heart
  • A heart is to the left of a spade

From left to right, what are the three playing cards?




8) The Money and the Hats

"No," said Jennifer to her 14-year old son Kyle. "I do not feel inclined to increase your allowance by $10 per week. However, if you're willing to take a risk, I'll make you a sporting proposition."

"What is it this time, Mom?"

"I happen to have," Jennifer said, "ten crisp new one-dollar bills and ten crisp new ten-dollar bills. You may divide them any way you please into two sets. We'll put one set into hat A and the other set into hat B. Then I'll blindfold you. I'll mix the contents of each hat and place each one on the table. You pick either hat at random and then reach into the hat and withdraw one bill. If it's a ten you may keep it."

"And if it isn't?"

"You wash my van once a week for a month with no complaints."

Kyle agreed. How should he distribute the 20 bills into the two hats to maximize the probability of drawing a ten-dollar bill and what will that probability be?




9) Saturday Night Poker

Five friends (Bill, Tom, Tex, Joe, and Steve) decide to liven up their weekly Saturday night poker game. They shuffle and deal the highest 25 cards (all 9's through aces, plus one 8) and when all the cards are dealt, the hands look like this:

Steve, who is not Mr. Brown nor Mr. Martin, has the best hand showing.

Mr. Martin knows that only Mr. Hill could have a better hand than he does.

Mr. Pike has a flush.

Joe knows that Bill only has two pair.

Tex, who is not Mr. Smith, has the 4th best hand.

Given the clues above, can you determine...
  • the player's first and last names?
  • the cards each player holds?
  • who has the best hand?




10) A MasterMind Puzzle (1)

For those of you who are fortunate enough to be familar with MasterMind, here's a rather simple MasterMind puzzle for you. Solve the hidden code.

Note: Regular MasterMind conditions apply:

  • 6 colors (green, red, yellow, brown, dark-blue, light-blue)
  • A black keypeg indicates that a code peg is the right color and in the right position
  • A white keypeg indicates one of the code pegs is the right color but in the wrong position