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

[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.

 

[Rahmuss]

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.

 

[AntonVrba]

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

 

[Rahmuss]

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...