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#169 A Domino Piazza

Some town squares are designed as giant chessboards, but urban planner Dominica has paved her town’s new piazza with giant dominoes instead.

Picking different dominoes at random from a set, she laid them down flat to form a 7×7 square of numbers (pictured, below), leaving one space in the centre for a fountain.

Using the numbers on the diagram, can you draw the outlines of the dominoes that Dominica used, and figure out which dominoes she left out? (Remember that a full set of dominoes contains every pair of numbers from 0-0 to 6-6. There were no duplicates).

#168 Bone Idle

Solution

Rick has to revise at least 11 topics. To figure out how many topics you need to study, imagine the worst-case scenario. In this palaeontology exam, the maximum number of topics that you could revise, only to find that none come up in the exam, is seven (18 topics minus 11 questions). So if Rick revises seven subjects, plus an additional four, then he will have at least four questions to choose from.

In general, if there are T topics, X exam questions and Q questions to be answered, then to be certain that at least Q of your topics will come up, the minimum number of topics N that a lazy student should revise is given by N = T – X + Q.