Geometry

Crumbs on a Table

by

A maid was about to wipe the crumbs off a rectangular table measuring 4 ft. by 8 ft. when the butler, a methodical type, took over. “You need a system!” he said. They both had very short arms and could only reach 2 feet with the dust cloth, so the butler decided to get all the crumbs together at center point C along one side. He walked along the opposite side, AB, pushing all the crumbs as far as he could directly toward C, and then did the same thing walking down each end; finally he went to the other long side to pull everything toward the dustpan. When he finished, the maid complained. Why?

Continue reading Crumbs on a Table →

Tangalese People Non-Toxic

by

The following three statements are true:

Tangalese people are non-toxic.
No person is a dingbat who can dance the hustle.
Non-toxic persons are dingbats.

Which of the following are true?

  1. Dingbats are Tangalese.
  2. Some Tangalese can dance the hustle.
  3. A person who cannot dance the hustle is toxic.
  4. No Tangalese person can dance the hustle.

Continue reading Tangalese People Non-Toxic →

Pickled Walnuts, Prof. Piltdown

by

On the assumption the following nine statements are factually correct, what conclusion, if any, can be drawn?

  1. Pickled walnuts are always provided at Professor Piltdown’s parties.
  2. No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street.
  3. All armadillos can speak the Basque dialect.
  4. No animal can be registered as a philatelist who does not carry a collapsible umbrella.
  5. Any animal that can speak Basque is eligible for the Tintinnabulum Club.
  6. Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
  7. All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
  8. The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s.
  9. Only animals that take taxis in Bond Street carry collapsible umbrellas.

Continue reading Pickled Walnuts, Prof. Piltdown →

True Statements on Card

by

Here is a card with the four statements that you see, and no others. Assume that each statement on the card is either true or false; then find and identify each false statement. (Refer to them as a, b, c, d if you want, to speed things up.)

On this card exactly one statement is true.
On this card exactly two statements are true.
On this card exactly three statements are true.
On this card exactly four statements are true.

Continue reading True Statements on Card →

Negation, Kmart Barbells

by

If the statement “All sets of barbells in Kmart are on sale” is false, then which of the following statements must be true?

  1. All sets of barbells in Kmart are not on sale.
  2. There is some set of barbells in Kmart that is not on sale.
  3. No set of barbells in Kmart is on sale.
  4. Not all sets of barbells in Kmart are on sale.
  1. II only
  2. IV only
  3. I and III only
  4. II and IV only
  5. I, II, and IV only

Continue reading Negation, Kmart Barbells →

Humber Bridge, Radius of Earth

by

The single-span suspension bridge crossing the estuary of the Humber River on the east coast of England has towers that are 162.5 meters tall (AC=BD). The span at sea level is 1410 meters (about 4/5 of a mile). The tops of the towers are 3.6 cm farther apart than the bases (i.e. AB=1410.036 m). What is the radius of the earth?

Continue reading Humber Bridge, Radius of Earth →