Line paradox. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Line paradox. Focus secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

Let's draw ten vertical lines of the same length on a rectangular sheet of paper and draw a diagonal with a dotted line:

Focus Paradox with lines

Let's look at the segments of these lines above and below the diagonal; it is easy to see that the length of the first decreases, and the second increases accordingly. Cut the rectangle along the dotted line and move the lower part to the left down:

Focus Paradox with lines

By counting the number of vertical lines, you will find that there are now nine. Which line disappeared and where? Move the left side back to its original position and the line that disappeared will reappear. But which line fell into place and where did it come from?

At first, these questions seem puzzling, but after a little reflection it becomes clear that no single line disappears or appears. What happens is that eight of the ten vertical lines are cut into two segments by a dashed line, and the resulting sixteen segments are "redistributed", forming (together with two unaffected vertical lines) nine lines, each of which is a little longer than the original ones. Since the increment in the length of each line is very small, it is not immediately apparent. In reality, the total value of these increments is exactly equal to the length of each of the original lines.

Perhaps the essence of the paradox will come out even more clearly if it is illustrated on pebbles. Take five piles of pebbles, four pebbles in a pile. Let's move one pebble from the second pile to the first, two pebbles from the third to the second, three from the fourth to the third, and finally all four pebbles from the fifth to the fourth:

Focus Paradox with lines

After such a shift, it turns out that there were only four piles. It is impossible to answer the question which pile disappeared, since the pebbles were redistributed so that each of the four piles had a pebble added. Exactly the same thing happens in the line paradox. When parts of the sheet are shifted diagonally, the segments of the cut lines are redistributed and each resulting line becomes slightly longer than the original.

Author: M.Gardner

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The Kuna Indians live on islands off the Caribbean coast of Panama. Unlike residents of developed countries, the representatives of the tribe rarely have hypertension, their blood pressure does not increase with age, and the frequency of diseases associated with high blood pressure - heart attack, diabetes, stroke - is lowered. But those Indians who have moved to the mainland are losing the islanders' protection against hypertension.

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