51. In modern times, valuables are kept in a safe that might have a combination lock. In Roman times, most valuables were stored in a strongbox (arca) that was anchored to the spot and locked with a key.
Can you figure out the combination to the safe from these clues? The first number, multiplied by 3, produces all ones; the second number, multiplied by 6, produces all twos; the third number, multiplied by 9, produces all threes.
52. The Forum Baths in Herculaneum are divided into two sections, and there are separate entrances for men and women. The bath complex offers the usual facilities: apodyterium (A), caldarium (C), tepidarium (T), frigidarium (F), and palaestra (P). Based on the following information, match the names of five patrons with their misplaced items and the locations in the baths shown on the floor plan below.
53. The Romans improved primitive counting boxes by using beads made of stone or ivory that slid on wires or in channels. Calculations were performed by moving them back and forth according to a set of rules. The Roman abacus even included a way to deal with fractions. The two grooves on the far right side of the abacus shown below were used to indicate fractions based on onetwelfth of the Roman system of units. It was small enough to fit in the pocket of a modern day shirt!
If a sum on the abacus were to be 4,524, how would it be written in Roman numerals?
54. Many of the houses in Pompeii used tile mosaics as decorations. Can you duplicate this Egyptian motif without lifting your pencil from the paper or crossing or retracing any lines?
55. Véronique returned from the macellum having spent 14 denarii on food for the Saturnalia banquet. The meat cost twice as much as the vegetables, and the vegetables cost twice as much as the fruit. At the time of her purchases, 1 gold aureus = 25 silver denarii = 100 brass sestertii = 400 bronze asses. How much did Véronique spend on vegetables?
56. An argentarius has 25 gold coins, but one of them is counterfeit and weighs less than the genuine coins. What is the minimum number of times that the banker must use his balance scale to determine which coin is fake?
57. 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 answer this question correctly."
58. The emperor Maximus wants to build an amphitheater on a site which contains the ruins of an old fortress. Only three pillars remain on the site, and the emperor wants to preserve them. He asks his architects to design a circular structure so that these pillars will be along its circumference. The distances of these pillars from each other are shown in the diagram on the right. What will be the radius of the amphitheater that is to be built?
59. A curious puzzle from the East called sudoku has been brought to Rome. Each row and column should contain one of each of the Roman numerals IVI. In addition, each of the shapes marked by thicker lines should also contain the Roman numerals IVI. Are you able to solve this Roman sudoku?
60. Tignarius is an ingenious carpenter. He was able to cut this square board into 4 smaller pieces that can be rearranged to form two smaller squares, each having half the area of the original square. Can you figure out his plan?
