Math Is Fun Forum

a 9 long, max=24
1 3 6 10 15 21 4 12 24

an 11 long, max=34
1 8 17 19 6 10 26 23 2 34
15

a 14 long, max=40
1 3 6 10 15 21 4 5 31 18
7 9 40 24

a 15 long, max=36
1 3 6 10 15 21 4 32 17 8
28 36 13 12 24

Well, I pick a random square and subtract last number from it
and check if number is used yet.
Here's 22 long (my favorite #), Max#41
1 3 6 10 15 21 4 12 13 23
2 7 9 27 22 14 11 25 24 40
41 8

a 19 long, max 46
1 3 6 10 15 21 4 12 13 23
2 7 29 20 5 31 18 46 35

Another Length 25, all #'s < 50
1 3 6 10 15 21 4 32 17 19
30 34 2 7 42 22 14 35 29 20
44 5 11 25 24

A twenty long, below 50
1 3 6 10 15 21 4 32 17 8
28 36 13 23 41 40 9 16 33 48

Length=25, #'s < 50
1 8 17 19 6 3 22 14 11 5
31 18 7 2 23 26 10 39 25 24
40 9 16 33 48

Length=21, #'s < 50
1 8 17 19 6 10 15 21 4 5
11 14 2 7 9 16 20 29 35 46
3

Totally rad! You must be breaking new ground.
I'll go over this more closely soon.  This is terrific!
How about an impulse function, a square wave that
occurs only once.  This could be used as a pass filter
to partition out certain parts of a function within a
certain range of x.  So instead of saying y=5 for 10 < x <20,
you could multiply by the square impulse.
Awesome work, krassi!

More to ponder.
1 3 13 12 4 5 11 14 2 7
9 16 20 29 35 46 18 31 33 48
52 69 75 6 10 15 21 28 8 17
19 30 34 47 53 68 32 49 51 70
74 26 23 41 40 24
forty-six long.

1 8 17 19 6 3 13 12 37 44
5 31 33 48 16 20 29 7 42 22
27 54 10 71 50 14 35 46 75 25
39 61 60 40 9 72 28 53 11 38
43 21 15 66 55 26 23 2 119 77
148 108 36 160 65 191 34 87 169 120
105 91 165 124 132 157 99 45 76 213
111 250 74 95 161 200 89 235 126 18
103 153 171 85 59 110 146 143 113 211
78 147 49 176 80 41 248 152 73 183
217 224 32 368 116 109 375 154 135 394
47 178 222 307 177 264 97 344 185 256
144 340 189 295 234 166 123 201 240 289
195 205 84 277 252 4 525 100 69 460
24 57 267 358 83 206 278 163 413 212
149 335 194 431 145 384 241 288 337 63
226 98 158 326 299 230 170 455 121 408
168 273 88 56 385 291 438 187 542 134
155 101 524 52 477 199 242 82 543 133
92 164 320 305 424 417 67 294 106 623
218 407 269 215 626 274 351 378 298 486
243 333 196 588 312 472 428 356 485 244
285 556 228 613 287 554 122 662 238 86
539 302 139 645 255 421 363 313 416 484
357 268 461 323

I like this one because it ends with 19 squared, which I always liked.
1 35 86 398 131 310 315 85 84 141
28 501 124 72 769 15 309 267 358 126
18 711 130 159 325 75 214 411 30 6
318 43 182 107 14 386 143 757 27 9
187 489 136 593 307 422 478 251 425 359
170 230 346 54 387 513 163 161 323 518
11 278 347 494 82 647 194 590 139 185
440 44 20 605 179 305 479 97 344 17
272 52 117 612 172 728 113 616 284 40
360

I thought I would join in the fun!!
1 63 337 192 169 56 88 537 363 478
51 30 114 142 587 197 532 368 161 239
17 152 689 40 744 156 205 524 5 779
121 168 361 39 25 119 77 599 130 654
246 195 705 79 362 214 147 177 223 218
566 275 454 171 153 72 9 187 438 238
387 13 663 237 163 462 267 574 2 23
146 754 87 442 399 330 295 434 466 375
250 74 767 133 36 189 67 609 120 556
285 4 357 543 82 494 235 606 70 11
278 206 470 430 354 546 183 493 236 440
136 188 653 131 769 15

I heard on the news, you folks in the UK just got a lot of snow!  Hope you like it.

I think anyone that can solve it without learning the solution tricks has got to be a genius!  Even learning the moves and when to apply them requires some aptitude, which I was able to handle.

Also, you could alternatively write
y= (x+5)(x-5) and solve for x, which is the average of the
two numbers you are looking for.
This might make the answer easier to see just by guessing.
Or continue.
y = x^2 - 25 and then logic tells you that x of zero makes y
turn out the smallest, because negative x's square to
positive numbers greater than the zero.