This came from a game of cribbage solitaire that I read about.

Five hands plus a starter card, all from the same deck, can score 127 points. Apparently there is only one combination of cards that can do this. What is it?

I figure that the hands probably score 24, 24, 24, 26, and 29. Obviously the 29 has the Nobs and the starter is a 5. What are the other hands?

It’s impossible to score 26 in a cribbage hand, so that can’t be it.

I’m thinking this is impossible. There are many ways of scoring 24 in a hand, but only one way of getting 28 or 29 (5555J or 5555N). So you couldn’t get more than one hand of 28 or 29 with a single deck. And since the next-highest possible score is 24, 127 is impossible with five hands (29 + 4*24 = 125). Even if you counted His Heels as the starter card (two points), you wouldn’t be able to get to 127 because no 24 scoring hand contains a ten card.

You’ve also got A7777, 33339, 36666, 44447, 44556, 45566, 67788, and 77889 as 24-point hands. The hard part, of course, is that if you have a 5 as the starter eventually you’re going to run out of 4’s and 6’s to fill out those 24-point hands comprised of different numbers of 4-5-6.

This is the best I came up with on short notice:

Starter: 5
Hands 4466 (24), 4466 (24), 555N (29), QQQQ (20), KKKK (20). That comes up as 117…perhaps that’s where your misremembering came in, as 127 instead of 117?

It could be. I’m racking my brain to think of another way to score more than two 24’s and one 28/29, which would be the only way to get a higher score. The problem is that if you want to score a 28/29, you have to have a 5 or a 10 as the starter. If you’ve got a 5 as the starter, you’re stuck with the 4-5-6 combos as your only potential 24’s…and your 28/29 has to be 555J/N, which takes away the rest of the 5’s. So that leaves only 4466 as your 24-point hands, and you can only do two of those. If you have a 10-card as your starter, you’re really stuck because there are no 24-point hands containing a 10.

Yeah, to be exactly one point shy of pegging out in Solitaire is really frustrating. But so is reality, sometimes.

Let’s work this out. The highest scoring Cribbage hands are 29, 28 and 24 points, and all the 24 point hands involve double double runs with interior 15s in the range of cards from 4-8 like you have here.

The only 29 point hand: N5555 (with 5 in the crib, N = Nobs in hand). This is known. (Though for purposes of this kind of solitaire scoring, I suppose turning up “Heels” with the Jack in the crib and having a hand of four 5s would actually score 30 points?)

All 28 point hands: Any other combination of all four 5s and a non-Nobs (or Heels) honor card.

All 24 point hands: A7777, 33339, 36666, 44447, 44556, 44566, 45566, 67788, 77889

You’ve got five 24 point hands sharing the same crib card. Can we do better? Well to do so, you’d have to substitute one of the 24 point hands with one of the 28 or 29 point hands - and all of those require tens and four 5s.

So let’s try to rejigger the hands so that the crib card is a 5, to allow for multiple 24-point hands involving 5s in four of the hands, along with (why not) the 29-point N555 in hand. But that would mean those four 24-point hands would have to be able to score 24 points with only one 5 (the one in the crib), since the fifth hand is using all the other 5s.

But, only one of the 24 point hands that include a 5 can do so with only one 5, leaving the other 3 in the cold. And there were only three such hands to begin with (never mind four).

Therefore, you can’t score better than five 24 point hands.

Yeah, when you come down to it, the problem is that if you want to score more than 120 from five hands, at least one of the hands has to be a 28 or 29. And if you set up the deck so that you have one of those two hands, you can’t make four other hands of 24. It’s as simple as that.

Yeah, maybe “cribbage solitaire” has some other way to score points than we’re thinking about - we’ll need some more info on just what that means in this context (I can find several variants with Google). For example maybe there’s a 4-card crib to score with the starter card as well (not just the 5 hands straight up)?

For example, the most common form of “Solitaire Cribbage” I’ve seen reference to online is a form called “Cribbage Squares” where you have not five, but FOUR hands and a starter card… BUT, you score in both rows and columns. And to “win” you need a score of 61, not 121.

This is actually a very interesting solitaire, I shall have to give it a try! On the other hand (ha) the perfect score at Cribbage Squares is 147, not 125.

The game I’m talking about is exactly as I described it in the OP. The challenge was to score 125 using that exact setup. No doubt there are other games that could score more, but that’s not the question.