Project Euler/253

From charlesreid1

Problem Statement

Tidying Up

A small child has a "tidying up" routine for his collection of 40 pieces. Starting with all pieces randomly arranged on the floor, he goes through the following process:

He divides the collection into a number of non-empty piles, then re-stacks the piles into a single pile. The child repeats this process until the pieces are in ascending order.

Let E(n) be the expected number of rounds needed to tidy up n pieces using this method, where the pile divisions are chosen uniformly at random.

Find E(40) and give your answer rounded to 6 decimal places.

Flags



Euler.jpg
Project Euler
project euler notes

Project Euler

Grid 0: Problems 1-99

Problem 1  · Problem 2  · Problem 3  · Problem 4  · Problem 5  · Problem 6  · Problem 7  · Problem 8  · Problem 9  · Problem 10

Problem 11  · Problem 12  · Problem 13  · Problem 14  · Problem 15  · Problem 16  · Problem 17  · Problem 18  · Problem 19  · Problem 20

Problem 27  · Problem 28  · Problem 29  · Problem 30

Problem 31  · Problem 32  · Problem 33  · Problem 40

Problem 41  · Problem 42  · Problem 43  · Problem 44  · Problem 45  · Problem 46  · Problem 47  · Problem 48  · Problem 49  · Problem 50

Problem 51  · Problem 52  · Problem 53  · Problem 54  · Problem 55  · Problem 56  · Problem 57  · Problem 58  · Problem 59  · Problem 60

Problem 61  · Problem 62  · Problem 63  · Problem 64  · Problem 65  · Problem 66  · Problem 67  · Problem 68  · Problem 69  · Problem 70

Grid 1: Problems 100-199

...

Problem 110  · Problem 111  · Problem 112  · Problem 113  · Problem 114  · Problem 115  · Problem 116  · Problem 117  · Problem 118  · Problem 119

Problem 150  · Problem 151  · Problem 152  · Problem 153  · Problem 154  · Problem 155  · Problem 156  · Problem 157  · Problem 158  · Problem 159

...

Problem 170  · Problem 171  · Problem 172  · Problem 173  · Problem 174  · Problem 175  · Problem 176  · Problem 177  · Problem 178  · Problem 179

...


Problem 190  · Problem 191  · Problem 192  · Problem 193  · Problem 194  · Problem 195  · Problem 196  · Problem 197  · Problem 198  · Problem 199


Grid 2: Problems 200-299

Problem 227  · Problem 254


Grid 3: Problems 300-399


Problem 301  · Problem 310

Problem 312  · Problem 319

Problem 323  · Problem 328

Problem 334  · Problem 337

Problem 345  · Problem 346

Problem 355  · Problem 356

Problem 364  · Problem 367

Problem 373  · Problem 378

Problem 382  · Problem 389

Problem 391

Grid 4: Problems 400-499

Problem 400


Grid 5: Problems 500-599

Problem 500  · Problem 501  · Problem 502


Grid 9: Problems 900-999

Problem 932


* = in progress

Flags  · Template:ProjectEulerFlag  · e


Retrieved from "https://charlesreid1.com/w/index.php?title=Project_Euler/253&oldid=30644"