The vestiges of the Roman Empire continue to evoke wonder. Remnants from this era have been extensively documented and, although exhaustively studied, questions still abound surrounding many aspects of daily life in those days. One of the most curious is why, especially during the early imperial period, the Romans used asymmetrical dice .
The human eye is able to distinguish the difference in size between two objects (e.g. two stripes or edges) when the variation between them is 5% or more. This is the case for the edges of the asymmetric shapes included in this challenge and that you should therefore be able to distinguish: which ones are not square?
The propensity to use these unique lopsided cubic pieces has generated various hypotheses, although historians and anthropologists have settled on three main ones:
One of the most popular dice-based logic problems is known as “ polar bears hunt seals ” (or alternatively “ petals around roses “). Here we present a Roman variant. The challenge is to find out what the response of a citizen of the Roman Empire would be.
A recent study offers a new approach to this Roman predilection for asymmetrical dice. To validate the probabilistic hypothesis, the researchers required a group of volunteers uninformed about the object of the experiment to label with dots replicas of Roman lopsided dice, following the usual configuration—already adopted in Roman times—in which the values of the opposite sides must add up to 7 (1-6; 3-4; 2-5). As the volunteers had no incentive or preconditioning to favour one number or the other, the authors of the study expected the labelling to be, on average, random. To their surprise, they found that the volunteers preferred to place the number 6 on the longer side, replicating the Roman pattern. When asked why, the answer was as logical as it was surprising: it is easier to paint the largest number of dots on the side with the largest surface area. Paradoxically, this explanation reinforces and nuances the least valued hypothesis, that of technical limitation.
And now what would be a Roman’s solution to these dice rolls of five in five?
Brainteaser 1: The asymmetric shapes are the ones coloured in red.
The result is the total of a number of Roman ones included in each roll:
As the name of the challenge suggests (Five Roman dice), the solution now reflects the number of Vs (the Roman number five) included in each roll.
Receive the OpenMind newsletter with all the latest contents published on our website
Receive the OpenMind newsletter with all the latest contents published on our website