### Alexandre Muñiz

Shared publicly -My exchange gift for the next Gathering for Gardner is a "magic" die. All numbers between 1 and 24 occur once. Faces sum to 50, bands around the cube sum to 100, and diagonal bands sum to 75.

After I had the dice in hand I thought of a way that I might have been able to make them more awesome. The upper left number on each face is a number between 1 and 6, so that the die can be used as a standard d6. We could think each of the positions on each face as 'modes' for rolling the dice. It would be really cool if the other three modes formed a set of non-transitive 'dice'. (Non-transitive dice are sets of three[1] dice where A usually beats B, B usually beats C, and C usually beats A.) It happens that the other modes in these dice do not form a non-transitive triple. I intend to search for a numbering of the dice that does make a non-transitive triple. This might require relaxing the constraints I put in for symmetry (of the positions used for the d6 mode) or for the diagonal bands. A "good" non-transitive triple would have margins of victory in the three contests that are balanced and relatively pronounced.

[1] Or more, but for our purposes three.

#g4g12

After I had the dice in hand I thought of a way that I might have been able to make them more awesome. The upper left number on each face is a number between 1 and 6, so that the die can be used as a standard d6. We could think each of the positions on each face as 'modes' for rolling the dice. It would be really cool if the other three modes formed a set of non-transitive 'dice'. (Non-transitive dice are sets of three[1] dice where A usually beats B, B usually beats C, and C usually beats A.) It happens that the other modes in these dice do not form a non-transitive triple. I intend to search for a numbering of the dice that does make a non-transitive triple. This might require relaxing the constraints I put in for symmetry (of the positions used for the d6 mode) or for the diagonal bands. A "good" non-transitive triple would have margins of victory in the three contests that are balanced and relatively pronounced.

[1] Or more, but for our purposes three.

#g4g12

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