## Shortest Path?

If you had to choose the shortest path from point A to point B, crossing the four squares with sides of 1 unit, which path would you take: the red one or the green one?

show solution

Captivate your audience with visual puzzles! Syndicated by @Knightfeatures, perfect for publishers seeking engaging content. Read more: https://knightfeatures.com/news-main/2017/1/5/gianni-sarcone

A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?

This puzzle is available as greeting cards from my online store.

## Prime Square

3,139,971,973,786,634,711,391,448,651,577,269,485,891,759,419,122,938,744,591,877,656,925,789,747,974,914,319,422,889,611,373,939,731 produces reversible primes in each row, column and diagonal when distributed in a 10×10 square.
Diagram by HT Jens Kruse Andersen.

## Mirror Squares

10² = 100 <-> 001 = 01²
11²  = 121  <->  121 = 11²
12² = 144 <-> 441 = 21²
13² = 169 <-> 961 = 31²

## Thébault’s theorem

If you place squares on the sides of any parallelogram, their centers will always form a square.

## Intriguing Geometric Dissections

Any two polygons with equal area can be dissected into a finite number of pieces to form each other. One of the most interesting dissection or geometric equidecomposition puzzles is that discovered by Harry Lindgren in 1951 (see Fig. 2 further below). As you know, in this kind of puzzles, the geometric invariant is the area, since when a polygon is cut and its pieces are distributed differently, the overall area doesn’t change.

Lindgren was the first to discover how to cut a dodecagon into a minimal number of pieces that could pave a square, when rearranged differently. His solution is very elegant, he first built a regular Euclidean pavement by cutting a dodecagon as shown in fig. 1.a, then arranging the four pieces symmetrically on the plane (fig 1.b). The tessellation achieved with these pieces corresponds, by superposition, to a regular paving of squares. The example in fig. 2 shows how the puzzle appears once finished.