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The Line Illusion (September 2026 Challenge Question)

Posted August 31, 2026 12:00 AM
Pathfinder Tags: challenge question

How many lines are there in these pictures? Explain the phenomenon depicted. (Apologies for the freehand Sharpie!)

Figure 1

Figure 2

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Rixter
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#1

Re: The Line Illusion (September 2026 Challenge Question)

08/31/2026 11:53 AM

The cut passes over the left hand stripe and under the right hand stripe. This makes it so that the end stripes are invisible when the paper is shifted.

Shifting the paper means that 1/9 of each stripe is doubled up, accounting for the missing stripe.
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silvCrow
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#2
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Re: The Line Illusion (September 2026 Challenge Question)

09/01/2026 12:40 AM

There are nine lines above the diagonal line and nine below it. The area of the lines in the top picture is the same as the ones in the bottom. The nine bottom picture lines are longer the the ten lines from the top picture.

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Rixter
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Re: The Line Illusion (September 2026 Challenge Question)

09/01/2026 3:45 AM

The cut divides the lines as follows: (TOP/BOT)

(0/9) (1/8) (2/7) (3/6) (4/5) (5/4) (6/3) (7/2) (8/1) (9/0)

After shifting:

(1/9) (2/8) (3/7) (4/6) (5/5) (6/4) (7/3) (8/2) (9/1)

10 lines, 9 units long become 9 lines, 10 units long
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#5
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Re: The Line Illusion (September 2026 Challenge Question)

09/05/2026 6:50 AM

“10 lines, 9 units long become 9 lines, 10 units long”

Very well stated. GA

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dkwarner
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Re: The Line Illusion (September 2026 Challenge Question)

09/01/2026 12:53 PM

There are 18 lines; 9 above the cut, and 9 below the cut. Shifting the papers for different horizontal alignments makes the lines below the cut align with either 8 or 9 of the lines above the cut, giving the appearance of 9 or 10 combined lines.

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