IBM Ponder This #262 · February 2020

In the famous Snakes and Ladders game, there is a board with 100 squares. You start at square 0 (just outside of the board) and then proceed to advance based on your move, which is dictacted by the throw of a fair dice. If your piece lands on a square that is at the very bottom of a ladder, you climb it. If your turn lands you at the head of a snake, you slide down to the bottom of its tail. And if your turn takes you out of the board (a square > 100), you stay in the square where you are at the time the dice was thrown.

Your challenge this month is to design a game with 10 ladders and snakes altogether that will lead to an expected number of moves (rounded to the 6th decimal place) of 66.978705.

Provide your answer as a list of 10 [source,target] pairs.

As an example, the standard game of 19, with 9 ladders and 10 snakes:
[1,38],[4,14],[9,31],[21,42],[28,84],[36,44],[51,67],[71,91],[80,100],[16,6],[47,26],[49,11],[56,53],[62,19],[64,60,],[87,24],[93,73],[95,75],[98,78] has an expected 39.225122 moves (again, rounded to the 6th decimal place).

Bonus '*' for getting to at least 12 digits after the decimal point to 66.978705007555420778.

Solution

Best opened after a real attempt

To be added.