# Try to Arrange Squares 1-24 into 70 Side Square Pyramid Puzzle

• chronon
In summary, there are 27 known solutions for a perfect square made up of 24 other squares, with side lengths ranging from 120 to 479. The least amount of perfect squares needed to make up a perfect square is 21, with the only known solution having side lengths of 112. It is possible to arrange the squares with sides 1 to 24 into one big square of side 70, but there are still 16 and 17 squares that cannot fit. There are no known solutions for perfect squares made up of 23 or 22 other squares, but it is possible that there are solutions for all numbers from 21 and above.
chronon
Following a post in the Number theory forum, I got to thinking: is it possible to arrange the squares with sides 1 to 24 into one big square of side 70. I think its probably impossible, but I've written an applet at http://www.chronon.org/applets/pyramid.html for people to try it out.

That's tough. I finally figured it out though... Yeah Right! The best I've been able to do so far was getting it down to the 16 and 17 squares as the only ones left. And the 16 square is actually pretty close to being able to fit in; but not the 17.

Cool App. How do you implement an Applet? I did a mortgage program and want to set it up as an applet.

there are 27 known solutions for for a perfect square made up of 24 other squares. The order 24 squares have side lengths as listed below and if a number is shown twice then two different solutions exist.
120 175 186 194 195 196 201 201 203 247 253 255 288 288 290 292 304 304 314 316 326 423 435 435 459 459 479

The least amount of perfect squares to make up a perfect square is 21 and the only known order 21 sqaure has sidelengths 112

AntonVrba said:
there are 27 known solutions for for a perfect square made up of 24 other squares. The order 24 squares have side lengths as listed below and if a number is shown twice then two different solutions exist.
120 175 186 194 195 196 201 201 203 247 253 255 288 288 290 292 304 304 314 316 326 423 435 435 459 459 479

The least amount of perfect squares to make up a perfect square is 21 and the only known order 21 sqaure has sidelengths 112

That's cool. Math is great. So did you configure one of the possible solutions? Are there solutions for 23 and 22? And if so, are there solutions for all numbers from 21 on? I guess I could do the math; but...

## 1. How do you solve the 70 Side Square Pyramid Puzzle?

The 70 Side Square Pyramid Puzzle can be solved by arranging the squares 1-24 in a specific order to create a pyramid with 70 sides. The exact method for solving the puzzle may vary, but generally involves starting with the base layer and working your way up to the top. It may also involve rotating and flipping some of the squares to fit into the pyramid structure.

## 2. Is the 70 Side Square Pyramid Puzzle mathematically possible to solve?

Yes, the 70 Side Square Pyramid Puzzle is mathematically possible to solve. While it may seem complicated and challenging, there is a specific solution that can be achieved by following a set of rules and techniques. It may take some trial and error, but with persistence and logical thinking, the puzzle can be solved.

## 3. What skills are needed to solve the 70 Side Square Pyramid Puzzle?

Solving the 70 Side Square Pyramid Puzzle requires a combination of spatial reasoning, problem-solving, and critical thinking skills. It also helps to have a good understanding of geometry and how shapes fit together. Patience and persistence are also important qualities to have when attempting to solve this puzzle.

## 4. Are there any tips or strategies for solving the 70 Side Square Pyramid Puzzle?

Some tips and strategies for solving the 70 Side Square Pyramid Puzzle include starting with the base layer and working your way up, using the numbers on the squares as clues, and trying different combinations to see what works. It can also be helpful to break the puzzle down into smaller sections and solve them one at a time.

## 5. Are there any real-life applications for the 70 Side Square Pyramid Puzzle?

While the 70 Side Square Pyramid Puzzle may seem like just a fun and challenging brain teaser, it actually has some real-life applications. This puzzle can help improve critical thinking skills and spatial reasoning abilities, which are useful in fields such as math, engineering, and architecture. It can also be a fun way to exercise the brain and keep the mind sharp.

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