61. Using only the digit 4, place sums of money in each of the 10 blocks of the pyramid in such a way that the grand total is 10,000 sesterces.
62. Students at a culinary school were invited to demonstrate their skills in a cooking contest; and the winner was to be awarded the Apicius prize. Each chef purchased 15 items, but no one bought the same number of items of the same sort to make a vegetable timbale. Based on the given price list and the following information, determine who won the award and what ingredients his recipe contained.
63. The solution to this magic square puzzle requires only two numbers. The middle row, the middle column, and both diagonals equal 19; all other rows and columns equal 30.
64. Trimalchio has six amphorae of Falernian wine to entertain his dinner guests. He wants to display them on a rack in the triclinium in such a way as to draw attention. Four or nine amphorae could form a square, but the placement of six is more complicated. Can you help place them so that an even number occurs in each occupied row and column?
65. For the Saturnalia, Véronique bought a 9-pound mixture of walnuts and almonds that cost 81.25 sestertii. The walnuts cost 25 asses per pound, and the almonds cost 45 asses per pound. At the time of her purchase, 1 gold aureus = 25 silver denarii = 100 brass sestertii = 400 bronze asses.
66. The Roman steelyard (statēra) was a type of balance. It consisted of a scaled arm suspended off center, a hook at the shorter end on which to hang the object being weighed, and a counterbalance at the longer end that could be moved to find the weight.
You are given 5 bags containing 10 coins in each bag. In four of the bags, the coins weigh 10 grams each. In the remaining bag, each coin weighs only 9 grams. You must find out which bag has the lighter coins. The problem is that all the bags look identical and all the coins look identical. You may use the statēra only once. How can you find out which bag has the lighter coins?
67. 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."
68. A wealthy patrician died and left his country estate to be divided among his wife and four children. If the estate is a perfect square, and the wife receives the part marked UX, how should the children divide the remainder so that each receives a parcel of the same dimensions and shape?
69. 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 I-VI. In addition, each of the shapes marked by thicker lines should also contain the Roman numerals I-VI. Are you able to solve this Roman sudoku?
70. Tignarius is an ingenious carpenter. He was able to cut this board into two pieces that are identical in size and shape. Can you figure out his plan?