_{This puzzle is a part of the Monthly Topic Challenge #3: Pencil and Paper Games}

Introducing a brand new tic-tac-toe variant of my very own devising (no less than I have never discovered an equal wherever on-line).

Background and instance

Xavier and Olivia are taking part in ‘Pigpen tic-tac-toe’. The sport is performed on a big tic-tac-toe grid (areas numbered 1 by 9), the place every of the 9 taking part in areas incorporates one other smaller tic-tac-toe mini-grid with areas labelled alphabetically, A by I:

On flip one, the beginning participant – Xavier, right here – spells out an actual phrase of two letters or extra utilizing solely the letters A by I, and – beginning with the mini-grid in house 1 – spells out the phrase so as, one letter per house, inserting their image on every letter that they use. For instance, if Xavier opened the sport with ‘BEIGE’, he would mark off the ‘B’ in mini-grid 1, the ‘E’ in mini-grid 2, the ‘I’ in mini-grid 3, the ‘G’ in mini-grid 4, and the ‘E’ in mini-grid 5, like so:

The second participant would then play a phrase of their very own, inserting the primary letter in the identical mini-grid wherein the earlier participant ended their flip. In our instance sport, since Xavier’s phrase completed in mini-grid 5, Olivia should place the primary letter of her phrase in mini-grid 5 additionally. Crucially, she can’t use a letter that has already been performed – in our instance sport, her phrase can’t start with the letter ‘E’. A legitimate play is likely to be ‘DEFACED’, for instance, which she then performs, wrapping spherical from mini-grid 9 to mini-grid 1 when required:

Players proceed, alternating turns, spelling out phrases utilizing unclaimed letters. If at any level they place three symbols in a straight line (horizontally, vertically, or diagonally) in the identical mini-grid – as per commonplace tic-tac-toe guidelines – they win that mini-grid and may declare the numbered house within the giant predominant grid for themselves, marking that with their image. That mini-grid is then retired and performs no additional half within the sport. When spelling out phrases in future turns, gamers merely skip over accomplished mini-grids and place their letter within the subsequent still-active mini-grid as an alternative. If a mini-grid is received on the ultimate letter of a phrase, the following participant locations the primary letter of their subsequent phrase within the subsequent still-active mini-grid as an alternative.

Summary of guidelines

1. Two gamers take it in turns to spell out phrases of two letters or extra utilizing unclaimed letters in consecutively-numbered mini-grids, one letter per grid. From mini-grid 9, play wraps round to mini-grid 1.
2. The first participant locations their first letter in mini-grid 1; all subsequent turns start utilizing the identical mini-grid wherein the earlier participant completed their flip*.
3. If a participant locations three equivalent symbols in a row inside the identical mini-grid, they win that grid and add their image within the corresponding house of the big predominant grid. Multiple mini-grids could also be accomplished on this manner inside the identical flip.
4. Mini-grids which were received by a participant – or have reached most capability and not using a winner – are retired from the sport and should be disregarded on subsequent turns, inserting the following letter within the subsequent still-active mini-grid as an alternative.
5. The sport ends when all mini-grids are received or crammed to capability and not using a winner, or when each gamers agree that no additional phrases could be performed.

_{* Unless a mini-grid is received on the ultimate letter of a phrase, wherein case the following participant locations the primary letter of their subsequent phrase within the subsequent still-active mini-grid as an alternative.}

Who wins? Well, there are two potential scoring variants:

Winning the sport:

In The Basic Variant, whichever participant claims probably the most particular person areas within the giant predominant tic-tac-toe grid is the winner.

In The Advanced Variant, gamers rating factors for areas claimed and contours of three symbols fashioned within the giant predominant tic-tac-toe grid: 1 level for every house claimed, plus a bonus of 5 factors for the primary participant to kind a line of three equivalent symbols in a row, and a bonus of three factors for every subsequent line of three equivalent symbols in a row. The winner is the participant with the best factors whole.

The puzzle

Here’s the factor – Xavier and Olivia cannot resolve which successful rule variant to play… Given clues to the phrases every of them performed throughout their turns (so as), beginning the sport from scratch, are you able to reconstruct the sport, and inform me whether or not the selection of successful rule variant would have made any distinction to the outcome?

X₁: Arrogant.
O₁: A horse’s meals holder.
X₂: An insect.
O₂: Stranded.
X₃: Performance.
O₃: Leader.
X₄: Large.
O₄: Husks.
X₅: Notion.
O₅: Offer.
X₆: “That man.”

Clue enumerations (so as of accelerating size): 2, 3, 3, 3, 4, 5, 5, 6, 7, 7, 9.