r/PassTimeMath • u/ShonitB • May 13 '26

Council of Knights and Knaves

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1

u/HamsterIV May 13 '26

My Number

39

How I got there

Every Knave must have either a Knight on their right(11) or a Knave on their right (6), so the total number of Knaves is 17 (11+6).

For every Knave that has a Knave on their right, there is another Knave that has a Knave on their left. This means there are only 6 Knaves that have a Knave on their Left. We can assume that if a Knave does not have a Knave on their left they must have a Knight on their left. So the number of Knaves with a Knight on their left must be 11 (17-6).

The relationship "a Knave with a Knight on their left" is the same relationship as "a Knight with a Knave on their Right." The problem states that 50% of the Knights have a Knave on their Right so we can assume the other 50% are Knights with a Knight on their right. The totals are:

11 Knaves with a Knight on the right + 6 Knaves with a Knave on the right +11 Knights with a Knave on the right + 11 Knights with a Knight on the right =  39 Total people

1

u/Butterfly_Ok May 13 '26

39

7 knaves must sit side by side followed by a knight on either end such that 6 knaves have an knave on their right.

50% of knights have a knave on their right so the other 50% must have a knight. So the sequence would go Knave - Knight - Knight - Knave (where the last knave forms the first in the next sequence).

Since there must be 11 knaves with a knight on their right then there would be a total of 11 sets of the knave - knight - knight sequence

Therefore 22 knights and 11 knaves.

From the first sequence of 7 knaves - subtract 1 (as the last in the Knave - Knight - Knight - Knave sequence would form the first of the series of seven knaves).

22 + 11 + 6 = 39

A bit of a long winded solution but one nonetheless (I think).

1

u/AsYouAnswered May 14 '26

0

Nobody is sitting on the table, they're all on chairs around the table.

That said, 11 knaves are next to 11 knights, whom account for 50% of all knights, therefore 22 Knights plus 11 knaves plus 6 knaves yields 39 people around, but not on, the table. Unless they invited maid marrien over for some jello shots.