yaworsw/euler-manager

---
:id: 298
:name: Selective Amnesia
:url: https://projecteuler.net/problem=298
:content: "Larry and Robin play a memory game involving of a sequence of random numbers
  between 1 and 10, inclusive, that are called out one at a time. Each player can
  remember up to 5 previous numbers. When the called number is in a player's memory,
  that player is awarded a point. If it's not, the player adds the called number to
  his memory, removing another number if his memory is full.\n\nBoth players start
  with empty memories. Both players always add new missed numbers to their memory
  but use a different strategy in deciding which number to remove:  \nLarry's strategy
  is to remove the number that hasn't been called in the longest time.  \nRobin's
  strategy is to remove the number that's been in the memory the longest time.\n\nExample
  game:\n\n<center><table class=\"p298\">\n<tr>\n<th>Turn</th>\n  <th>Called<br>number</th>\n
  \ <th style=\"text-align:right;\">Larry's<br>memory</th>\n  <th>Larry's<br>score</th>\n
  \ <th style=\"text-align:right;\">Robin's<br>memory</th>\n  <th>Robin's<br>score</th>\n</tr>\n<tr>\n<td>1</td>\n
  \ <td>1</td>\n  <td style=\"text-align:right;\">1</td>\n  <td>0</td>\n  <td style=\"text-align:right;\">1</td>\n
  \ <td>0</td>\n</tr>\n<tr>\n<td>2</td>\n  <td>2</td>\n  <td style=\"text-align:right;\">1,2</td>\n
  \ <td>0</td>\n  <td style=\"text-align:right;\">1,2</td>\n  <td>0</td>\n</tr>\n<tr>\n<td>3</td>\n
  \ <td>4</td>\n  <td style=\"text-align:right;\">1,2,4</td>\n  <td>0</td>\n  <td
  style=\"text-align:right;\">1,2,4</td>\n  <td>0</td>\n</tr>\n<tr>\n<td>4</td>\n
  \ <td>6</td>\n  <td style=\"text-align:right;\">1,2,4,6</td>\n  <td>0</td>\n  <td
  style=\"text-align:right;\">1,2,4,6</td>\n  <td>0</td>\n</tr>\n<tr>\n<td>5</td>\n
  \ <td>1</td>\n  <td style=\"text-align:right;\">1,2,4,6</td>\n  <td>1</td>\n  <td
  style=\"text-align:right;\">1,2,4,6</td>\n  <td>1</td>\n</tr>\n<tr>\n<td>6</td>\n
  \ <td>8</td>\n  <td style=\"text-align:right;\">1,2,4,6,8</td>\n  <td>1</td>\n  <td
  style=\"text-align:right;\">1,2,4,6,8</td>\n  <td>1</td>\n</tr>\n<tr>\n<td>7</td>\n
  \ <td>10</td>\n  <td style=\"text-align:right;\">1,4,6,8,10</td>\n  <td>1</td>\n
  \ <td style=\"text-align:right;\">2,4,6,8,10</td>\n  <td>1</td>\n</tr>\n<tr>\n<td>8</td>\n
  \ <td>2</td>\n  <td style=\"text-align:right;\">1,2,6,8,10</td>\n  <td>1</td>\n
  \ <td style=\"text-align:right;\">2,4,6,8,10</td>\n  <td>2</td>\n</tr>\n<tr>\n<td>9</td>\n
  \ <td>4</td>\n  <td style=\"text-align:right;\">1,2,4,8,10</td>\n  <td>1</td>\n
  \ <td style=\"text-align:right;\">2,4,6,8,10</td>\n  <td>3</td>\n</tr>\n<tr>\n<td>10</td>\n
  \ <td>1</td>\n  <td style=\"text-align:right;\">1,2,4,8,10</td>\n  <td>2</td>\n
  \ <td style=\"text-align:right;\">1,4,6,8,10</td>\n  <td>3</td>\n</tr>\n</table></center>\n\nDenoting
  Larry's score by <var>L</var> and Robin's score by <var>R</var>, what is the expected
  value of |<var>L</var>-<var>R</var>| after 50 turns? Give your answer rounded to
  eight decimal places using the format x.xxxxxxxx .\n\n"