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HomeEntertainment NewsThe trisablier, the mathematical enigma of “World” No. 27

The trisablier, the mathematical enigma of “World” No. 27

A trisable works like an hourglass, except it is made up of three compartments. It can then be placed in two positions: with one compartment above and two below (as in figure A), or with two compartments above and one below (as in figure B). In the first case, the flowing sand is evenly distributed between the two lower compartments. In the second position, the two upper compartments flow into the lower one at the same time.

The hourglass illustrated by the figures contains exactly eight minutes of sand.

So, in position A, the sand will flow for eight minutes and each bottom compartment will contain four minutes of sand. In position B, the left compartment will be emptied in six minutes and the right compartment in two minutes. After six minutes, all the sand will be at the bottom.

Initially all the sand is in the same compartment, can you measure a time of five minutes with this hourglass?

Can you imagine a method to measure any integer number of minutes?

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The following figure shows how, from the initial position, it is possible to isolate any integer number of minutes between 1 and 7. Each position is obtained from the previous one by rotating the hourglass a third of a turn in one direction or another. . To measure 5 minutes, simply take the position at the bottom left and then place the compartment containing 5 minutes on top. With all these positions it is possible to measure any integer number of minutes.
To do this, start by measuring the remainder of this number by dividing by 8 with one of the positions in the figure, then repeat the full 8 minutes as many times as necessary. For example, to measure 18 minutes. Start by measuring 2 minutes from the middle position, then continue with two full 8-minute periods. Note, however, that to chain these 8-minute periods, care must be taken not to divide the 8 minutes into 2 as in the first position, but to make them flow into a single compartment.

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Anthony Robbins
Anthony Robbins
Anthony Robbins is a tech-savvy blogger and digital influencer known for breaking down complex technology trends and innovations into accessible insights.
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