What are the fewest pre-measured weights that would be needed to measure any exact number of ounces from 1 to 120?

42. For most Romans, home was an *insula*, a multi-storied apartment building that might occupy an entire block. Tenants usually rented the small rooms (*cenacula*) built over the shops on the ground floor, but it was possible to buy a room or a floor outright. Based on the following information, match the names of six tenants with their occupations and the locations of their shops on the floor plan of the *insula* shown on the right.

The barber's shop is on a corner.

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43. One of several systems used for dating years in the Roman era was based on the founding of the city of Rome: *ab urbe condita* (AUC). According to tradition, that happened in 753 BC. How would the date AD 2005 be expressed in Roman numerals AUC?

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44. Many of the houses in Pompeii used tile mosaics as decorations. Can you duplicate this design for a mosaic floor without lifting your pencil from the paper or crossing or retracing any lines?

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45. Scintilla returned home after a day of shopping and discovered a total of 71 coins in her *saccus*. At the time of her purchases, 1 gold *aureus* = 25 silver *denarii* = 100 brass *sestertii* = 400 bronze *asses*.

If the money had a value of 3½ *aurei*, how many coins of each type were in her purse?

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46. An *argentarius* has three *denarii*, one of which is counterfeit and heavier than the genuine coins. Using his balance scale only once, how can the banker determine which coin is fake?

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47. Prior to a meeting of the Senate, Gaius Perplexus challenged the assembly with this proposal: "I'll give an amphora of wine to the first citizen who can give a solution to this riddle."

Which letter of the alphabet is most like a

Roman emperor?

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48. The owner of a seaside villa has been murdered! The visitors to his *domus* that day were Aulus, Brutus, and Claudius; Falco suspects that one of them is the murderer. He shows these statements from various household slaves to Helena.

a. The murderer arrived at the villa later than at least one of the other two visitors.

b. One of the visitors, a lawyer, arrived at the villa at midnight and earlier than at least one of the other two visitors.

c. Neither Aulus nor Brutus arrived at the villa after midnight.

d. The earlier arriver of Brutus and Claudius was not the lawyer.

e. The later arriver of Aulus and Claudius was not the murderer.

Helen thought for a moment and said, "Then the murderer must have been...." But the baby started to wail, and Falco couldn't hear the name. Can you help him?

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49. By the late republic, several marks were used in conjunction with Roman numerals. A bar above a number multiplied it by 1,000; lateral lines were added to denote 100,000. It was also common to use the superimposed bars in two other ways:

· to distinguish numbers from letters in composite words () and

· to denote numbers being used as adverbs ().

Based on this information, what number does represent?

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50. A tangram is a Chinese puzzle consisting of a square cut into seven pieces to be reassembled into different figures.

Can you rearrange the pieces to form each of these Chinamen? The second one is a "foot" shorter, but both figures contain all seven pieces.

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