In a similar vein to my previous puzzle Counter Game, there are a number of counters on the table, but this time you can either remove 2 or 7 of them on each turn. For instance if there were 11 counter there are three solutions: 2,2,7; 2,7,2; 7,2,2; (as before removing 7 then 2 is distinct from removing 2 then 7). Some numbers of counters have no solution, for instance if there are 5 counters you cannot remove them all.

If the number of counters is high enough, there are always more different ways to remove all the counters than to leave one counter behind, but this is not true for some smaller numbers, for instance if there were 12 counters there is only one way of removing them all (2,2,2,2,2,2), but as we have seen, three ways of removing 11 and leaving 1 behind.

What is the highest number of counters, for which there are fewer ways to remove them all than to leave one remaining?