111. Six matches can be arranged to create a regular hexagon.
With the addition of three more matches, can you arrange another regular six-sided figure?
a laurel crown.
113. Dionysus poses a challenge to you. Can you draw this figure of a grape cluster and leaf without lifting your pencil from the paper, retracing any lines, or crossing them?
114. Can you draw this figure without lifting your pencil from the paper, retracing any lines, or crossing them?
115. A generous Roman patron set aside a certain sum of money each week for equal distribution to his clients. One day he remarked "If there are five fewer clients next week, you will each receive two more sestertii." Unfortunately, there were four more clients the next week, so each received one sestertius less than before.
How much did each client receive at the last weekly dole?
116. An argentarius suspects that 1 of the 12 denarii which he received at his booth that day is counterfeit, but he is not sure if it weighs too much or too little.. Using a scale, but no weights, what is the minimum number of steps needed for the banker to tell which coin is counterfeit and whether it is too heavy or too light?
117. 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."
118. A wine merchant died and left the inventory of his taberna to be divided equally among his three sons. Seven of the amphorae were full, seven were half-full, and seven were empty. How can they be divided so that each son receives the same number of amphorae and the same amount of wine without changing their contents?
120. Tignarius is an ingenious carpenter. He cut a six-pointed star into five pieces that could be reassembled to form a perfect square. Can you figure out his plan?