Short description

In the image below, there are two sets of points, green and red. One of them is "random" while another one has been produced by me via clicking points into the square. Market resolves to YES if the green one has been produced by me and NO otherwise.

All 100 points have now been revealed

Details

One of the point sets has been produced by sampling from a uniform distribution over a square. The length of this square is strictly less than the bounding box in the square above. Call this the Hidden Square. I won't tell you the side length of the Hidden Square.

Another of these point sets has been produced by sampling from me. Some details of the data generation process:

• The points were generated by clicking a location in a UI interface on a mousepad.

• I generated 100 points in roughly 90 seconds.

• I have practiced.

• If a point landed outside of the Hidden Square, I discarded that point and generated a new one.

• I have applied one or several entropy-increasing transformations to the final point set.

To elaborate on the last point, here is a hypothetical example of such a transformation: "Given a point, round its x-coordinate to the nearest multiple of 10, and then add a uniformly random integer between 0-9 to it." Intuitively, this makes the set of points "more random", i.e. harder to distinguish from the "actually random set".

I won't tell which transformations I've used.

EDIT: Here are the transformations I used:

1. Reflect the points along the two perpendicular bisectors of the sides and one of the diagonals (giving 8 possible destinations for the point), in a uniformly random way.

2. Reveal the points in a random order, in a uniformly random way.

The length of the hidden square is 400 - 6*2, with the same center as the bounding box.

Other

Here is a market on how many points it will take for traders to figure out the answer: https://manifold.markets/Loppukilpailija/how-many-points-are-needed-to-disti-74e061c28bb6

The data

The data in a more convenient form. The bounding box in the image has corners at (100, 100) and (500, 500).

GREEN:

226 280

253 454

150 465

405 217

456 203

370 268

373 260

454 170

166 474

274 247

272 377

446 459

281 434

116 385

464 250

299 396

446 271

271 473

354 281

149 304

424 303

180 220

130 454

344 304

409 154

231 256

462 195

311 459

299 272

465 374

434 220

157 268

227 230

446 182

337 416

244 478

280 284

203 240

249 482

279 356

154 463

435 288

275 357

305 252

357 200

219 166

379 390

451 438

453 436

303 270

488 165

112 440

414 233

386 269

314 415

306 324

308 447

372 202

386 391

404 247

452 277

364 204

176 399

281 462

156 227

290 410

327 245

310 140

378 220

445 455

124 300

491 417

365 441

116 277

311 205

494 166

290 375

276 314

357 151

322 392

452 345

370 162

327 437

336 337

308 275

221 430

423 242

324 238

300 305

160 209

203 127

444 333

349 486

293 239

345 370

211 228

154 240

221 108

349 440

242 179

RED:

285 229

142 422

250 224

468 169

410 215

301 178

232 247

371 480

417 294

410 196

128 122

213 302

400 399

444 373

163 213

155 454

340 319

477 386

149 369

302 442

204 470

396 152

123 306

118 454

106 110

362 399

127 209

448 346

188 286

442 135

263 124

452 351

183 429

285 150

209 405

283 236

453 132

332 374

296 176

227 202

251 480

325 322

350 242

270 341

147 368

469 266

281 167

418 165

449 416

223 158

265 171

239 433

462 398

110 241

345 318

210 167

291 477

295 125

381 236

487 362

359 117

381 283

289 205

349 393

183 244

479 447

200 480

224 144

433 427

133 346

374 206

127 413

246 399

457 155

247 251

299 292

163 142

367 344

276 349

364 302

167 340

423 133

424 427

204 245

150 385

170 258

133 361

357 200

361 307

176 175

304 148

223 163

366 169

437 437

239 123

355 465

211 283

341 469

235 486

287 488