This is a standard, 4-player game of the board game 7 Wonders. The position of the players and their starting cities are given. Also given are the four actions taken on each turn, although (with a few exceptions) it is not specified who took which action. The entire game can be logically reconstructed (see below for detailed walkthrough) from this information. The proper assignment is:
At game’s end, the scoresheet looks like:
Applying the transformations from the scoresheet image and converting 1 to A, 2 to B, etc., gives the message COINS BETWEEN AGES (SPELL OUT THE DIGIT). Looking at the number of coins each player has at the points between Ages I/II and II/III, again converting to letters, and reading in the same order around the table, gives the phrase GAME NAME. The “game name” is of course “7 Wonders,” and spelling out the digit as instructed yields the final answer SEVEN WONDERS.
To begin, there appears to be no papyrus until the Press appears in II-5. So how does the Scriptorium get built in I-4? This is only possible if a Press has entered the game before I-4, and the only way that can happen is if Hal builds a press using the first stage of his wonder in I-3. (Incidentally this Press must have been the card sold in I-2.)
With that established, we turn our attention to clay. The only card that can produce clay is the Caravansery built in II-6. The first stage of Hal’s wonder is spoken for, and he can’t reach the second stage without multiple clay. Thus, no other clay-producing card can ever enter the game, and no one will spend clay on any purchase, other than potentially the owner of the Caravansery during Age III.
In I-3, there are not yet two stone in the game, so Alex can’t build her first stage. Thus, the other three must, and Alex builds the Theater in I-3. Nobody can build the second stage of their wonder in I-5 (Hal and Rhoda would need clay, Alex can’t access Rhoda’s gold), so Alex builds her first stage in I-5.
Alex, Ollie, and Rhoda must all have access to the Timber Yard in order to build their first stages, so the Timber Yard must be played by Ollie in I-2.
Rhoda’s I-1 play is known, so she must make a play in I-2 that allows her to buy two wood from Ollie in I-3 to build her first stage. Thus, Rhoda sells a card in I-2.
Hal needs to get two ore from Rhoda in I-3 to build his first stage. The remaining available cards in I-2 are no help, so he can only afford this if he builds the East Trading Post in I-1.
Note that we know the eventual locations of all the resources in Age I, except the Stone Pit. So we can briefly look ahead to Age II. The Training Ground in II-1 cannot be built by Hal (no access to wood) or Alex (no access to gold); therefore, it is built by Rhoda. The Courthouse in II-1 must be built via chain (no clay), so it must be built by the player who played the Scriptorium in I-4. This can’t be Alex (who plays a different card in I-4); therefore, it is Hal who plays the Courthouse in II-1 and the Scriptorium in 1-4. By elimination, Alex plays the Glassworks in II-1.
The Stone Pit in I-4 must be played where Alex can access it for her wonder stage buy in I-5; therefore, it is played by Ollie and not Rhoda. Rhoda plays the Altar in I-4.
Hal cannot play the Baths in I-5 (no access to stone), so Rhoda does. Hal sells in I-5.
Now consider Alex’s money situation heading into I-5. She needs two coins to pay for her wonder stage (using the West Trading Post), and no one can pay her any money before this (the only resource she has is glass, and the only card which requires glass is the Workshop which doesn’t appear until I-6). Thus, she cannot afford to pay two coins for either the Stockade in I-1 or the Apothecary in I-2 and still have enough money to pay for her wonder stage in I-5. Therefore, Alex buys the Pawnshop in I-1 and the Marketplace in I-2. By elimination, Ollie plays the Stockade in I-1 and Hal plays the Apothecary in 1-2.
In II-2, the Temple must be built via chain (no clay) by Rhoda. The Stables in II-2 must be built via chain (no clay) by Hal.
Hal cannot play the Aqueduct or Walls (can’t access enough stone) in II-4, or the School (no access to wood); therefore, he plays the Dispensary in II-4. That means he cannot play the Dispensary in II-3; neither can Alex (no access to gold) or Rhoda (no access to glass). Therefore, Ollie plays the Dispensary in II-3.
The Laboratory in II-2 must be built by chain from the Workshop in I-6, this leaves only Alex or Ollie as potentially playing the Workshop. Therefore, Hal and Rhoda cannot buy the Archery Range by chain in II-3. Can either buy it by resources? Hal cannot (no access to wood). Rhoda has two coins after I-5, and spends two coins in II-1. She can earn at most three coins from selling in I-6, and cannot earn any money in II-2 (no one buying gold). Thus, she has at most three coins in II-3, and cannot afford the Archery Range (which would cost her four). Therefore, Alex plays the Archery Range in II-3.
Alex has no access to gold, so she must have bought the Archery Range via chain. Therefore, Alex played the Workshop in I-6; the others sold cards in I-6. Alex plays the Laboratory in II-2 by chain. By elimination, Ollie plays the Quarry in II-2.
In II-3, Rhoda, with three coins, cannot afford the Library; Rhoda plays the Loom and Hal plays the Library.
In II-4, Alex, with three coins, cannot afford the Walls or Aqueduct; Alex plays the School.
The Forum in II-5 must be bought by chain, and Hal is already selling a card, so Alex builds the Forum. By elimination, Ollie sells a card in II-5.
In II-6, the second stage wonder cannot be built by Alex (no access to gold) or Hal or Rhoda (no clay); it is built by Ollie. With no wood, Hal cannot build the Caravansery or the Statue in II-6; he sells a card. The Statue cannot be built by Alex (no gold); it is built by Rhoda. Alex plays the Caravansery.
Rhoda must pay two coins to build the Statue in II-6, and she has seven coins after II-3. Thus, she cannot spend six coins on the Walls in II-4. Rhoda plays the Aqueduct in II-4 and Ollie plays the Walls.
In Age III, Hal’s plays each turn are essentially forced from the fact that he has no access to wood or stone. He must play the Lodge, Senate, University, Observatory, and Traders Guild on turns 2-6, and thus, must play the Arena on turn 1 (not a second University).
In III-1, Alex, with one coin, cannot afford the Arsenal or Shipowners Guild, so she plays the University. Rhoda cannot play the Shipowners Guild (no access to glass) so she plays the Arsenal, and Ollie the Shipowners Guild.
In III-6, Rhoda cannot play the Siege Workshop or Arsenal (already has one); she plays the Gardens. The Siege Workshop must be played by chain (not enough clay), so it is played by Alex. By elimination, Ollie plays the Arsenal.
In III-2, Alex cannot buy the Gardens (no clay) or the Strategists Guild (no second gold), so she plays the Town Hall. Rhoda can’t play the Gardens in III-2 (she plays it in III-6), so she plays the Strategists Guild. Ollie plays the Gardens, which he must do using his one free buy.
In III-3, Alex, being broke, cannot afford the Fortifications or the Circus; she plays the Haven. Rhoda, with one coin, cannot afford the Fortifications; she plays the Circus. Ollie plays the Fortifications.
The Pantheon in III-4 must be played by chain (no second clay) by Rhoda. Alex, unable to afford the Magistrates Guild (still broke), plays the Study. Ollie plays the Magistrates Guild.
In III-5, Alex, still broke, cannot afford the Craftsmens Guild and has already built a Haven; she plays the Academy. Rhoda, with three coins, cannot quite afford the Craftsmens Guild; she plays the Haven. Ollie plays the Craftsmens Guild.