On the six sides of the cube are the numbers a, b, c, d, e, and, ordered by size, if the cube with the largest number of the letter f is facing down, then the mean value of the numbers on the other five faces is 1. If The second largest number e is lower. Instead, the average of the other five numbers rises to 2.

Thus, the difference between the numbers f and e is exactly 5. If the third largest number d is less, then the average of the other five numbers increases to 3, which means that the difference between the numbers e and d is also exactly 5. This also applies to all other 4 pairs of adjacent numbers: the largest is always 5 greater than the smallest.

Since the average of the five smallest numbers on the cube must be 1, 1 = (a + b + c + d + e) / 5 = (a + (a + 5) + (a + 10) + (a + 15) )) + (a + 20)) / 5 = a + 10, which can be converted to a = –9.

Thus, the six numbers on the faces of the dice are –9, –4, 1, 6, 11 and 16. Instead of numbers, such dice can also be provided with eyes using plus and minus signs as the sums on the bank black and red phrases that are expressed .

These dice are not just a math gimmick, they can actually be bought. Trick Dice in Inverness in Scotland is manufactured and sold worldwide under the name hemi dice.

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