Math Problems

Its no fun if you just click the solution button before trying to solve them first.


The sum of Mike's age and Ed's age is 44 years.   Mike is twice as old as Ed was when Mike was half as old as Ed will be when Ed is three times as old as Mike was when Mike was three times as old as Ed.

 

How old is Mike?

Can you tell by quick inspection who is older?


 

 

This region is three quarters of a perfect square.

 

 

 

Subdivide this region into four regions of equal shape with equal areas.


You have 12 billiard balls all weighing the same except for one.

Using a balance for only three separate weighings tell which ball has the unique weight and whether it is heavier or lighter than the other eleven balls.

This must be shown for all possible cases.


There are 5 houses in five different colors.   In each house lives a person with a different nationality.   These five owners drink a certain drink, smoke a certain brand of cigar,

and keep a certain pet.   No owners have the same pet, smoke the same brand of cigar or drink the same drink.

 

The question is --- who owns the fish?

 

Summary:

Nationalities:       Norwegian, Dane, Brit, German, Swede

House colors:     Yellow, Blue, Red, Green, White

Drinks:                 water. tea, milk, coffee, beer

Cigars:                 Dunhill, Blend, Pall Mal, Prince, Blue Master

Pets:                    cats, horses, birds, fish, dogs

 

Clues:

the Norwegian lives in the first house

the Norwegian lives next to the blue house

the Brit lives in the red house

the Swede keeps dogs as pets

the Dane drinks tea

the German smokes Prince

the green house is on the left of the white house

the green house owner drinks coffee

the person who smokes Pall Mal rears birds

the owner of the yellow house smokes Dunhill

the man who keeps horses lives next to the one who smokes Dunhill

the man living in the house right in the center drinks milk

the man who smokes Blends lives next to the one who keeps cats

the man who smokes Blend has a neighbor who drinks water

the owner who smokes Blue Master drinks beer


You are traveling down a road until the road splits into two.   You know that one branch is the road leading to everything good and the other branch is the road leading to everything bad.   At the start of each branch is a man. One man is good and tells the truth 100% of the time.   The other man is evil and tells lies 100% of the time.   The good man does not necessarily stand on the road that leads to everything good.   You have only one question that can only have a "yes" or "no" answer that you may ask of only one of the men without knowing which man is good or evil.   Based upon the answer to your question you will know which road to go down to always get to everything good.

What is the question you should ask and what road do you go down based upon the answer?

Show this for all four possible cases.


 

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