Mental Exercise

Hairy Logic

A traveler arrives in a new town needing a haircut. The town has two barbershops. Being very particular about his hair, the traveler investigates both shops. The first barbershop is very clean and the barber has a very nice haircut. The second shop is messy with lots of hair on the floor and the barber has an uneven haircut. Which shop does the traveler choose for his haircut?

Tertiary Fraction

The digits 1, 2, 3, and 6 can be arranged as a fraction that equals one-third:

      12          1

     -----   =   ---

      36          3

Can you arrange the digits from one through nine:
1, 2, 3, 4, 5, 6, 7, 8, and 9 to similarly equal a fraction of one-third?

Switches and Bulbs

You are in a room with three switches. In another room that you cannot see, are three bulbs each of which can be turned on or off by each of the switches. The task is to figure out which switch controls which bulb by flipping switches and only checking the room with the bulbs once.

What if there are four switches and four bulbs, can the task still be accomplished by checking the room with the bulbs just once?

Anagrammed States

Take all of the letters use to spell out the names of  two different states and rearrange these letters to spell out the names of two other states. It is easy once you hit on the right strategy.

Secret Code

What could these strange symbols be, some secret code? Actually they are a series of five symbols starting at the top and going down. What is the sixth symbol? It is quite simple once you look at it the right way.

Puzzling Inheritance

Four heirs have inherited a parcel of land that is twelve acres in size. The will stipulates that the land must be divided evenly into four similarly shaped parcels. How can the surveyor divide this land into four identically shaped areas.?

Twin Paradox

Two girls are born to the same mother on the same day of the same year. Yet the girls are not twins. How is this possible?

Answers

Hairy Logic. The traveler chooses the messy shop. Since each barber must cut the hair of the barber in the other shop, the messy shop’s barber gives the best haircut. Also, the messy shop gets lots of business, with no time to even clean the hair off the floor.

Tertiary Fraction.   5832/17496 = 1/3

Switches and Bulbs.  Turn on switches 1 and 2 for several minutes, then turn switch 2 off. Turn on switch 3 and go check the room. Two of the bulbs will be warm, the warm one that is lit goes with switch 1, the warm one that is unlit goes with switch 2. Of the two cool bulbs, the lit one goes with switch 3 the unlit with switch 4.

Anagramed States. The letters of North Carolina and South Dakota rearrange to form South Carolina and North Dakota.

Secret Code.  Each symbol is composed of two copies of a letter of the English alphabet laid on their sides and stuck together. The next symbol in the series would be base on F and look like this:

Puzzling Inheritance.  The land can be divided like this

Twin Paradox.  The girls are part of a set of triplets.