This is correct.
The App he chooses is $14. The group includes (8.5, 12.5, 12.5, 14, 14, 20)
He is then directed to soups and chooses $10.50. (10.5, 14.5, 16.5, 16.5, 16.5)
His total at this point is $24.50.
He is then turned to grilled meats and chooses $32 (32, 32, 40, 40 (possibly others offscreen))
His total at this point is $56.50.
Then cakes for 14.50 (14.5, 14.5, 18.5 (possibly others offscreen))
Then dessert wines (all 12)
Ignored categories:
Salad (12,12,16,18 (possibly others out off screen))
Bread (4.5, 8.5, 10.5, 10.5)
Pasta (16, 16, 20, 22)
Specials (36, 36 (probably others off screen))
Mains (26, 26, 34, 34)
Desserts (6.5, 6.5, 10.5, 10.5)
Aperitifs (not shown, but also fixed price)
Could be a back of the menu too, if needed
There are two final categories that allow him to do a final adjustment if the total ends up too low. All of the later categories also all seem to feature only two prices - limiting price variation. The earlier ones have more variety, but also have repetition so that a certain price is more likely and he doesn’t have to goto categories like “bread” as often, which might seem a bit harder to fit into patter as part of a typical meal.
The two prices of mains (26/34) are $8 apart. The two prices of meats (32/40) are also $8 apart. The mains and the meats are $6 apart.
So, for example, if he had chosen the $16.50 soup instead of the $10.50 soup, Denny could have asked him to choose a main instead of a meat and been at the same point in the math.
The desserts (6.5./10.5) are $4 apart, as are the cakes (14.5 and 18.5) - the two are $8 apart from each other.
So if he had chosen the meat that was $40 instead of $32, he would have gone to the ‘desserts’ instead of the ‘cakes’ and again been at the same place in the math.
We can’t see the price of the Aperitifs, but I am confident that the price would have been $8.00 for all drinks. When George picks the $4 cheaper cake, he directs him to the $12.00 dessert wine section. If he had picked the $4 more cake, he would need a category that was $4.00 to still hit $83.00.
We can extrapolate the rest of the routine from that. The prices in the soups are all $6 more than the prices in the breads, so if he had chosen the $20 app instead of the $14 app, he would have gone to the breads instead of the soups to offset the $6 spend in the apps. If George had chosen a $12.50 app ($2.50 less), he’d have gone instead to the salads ($2.50 more than the soups). And for $8.5 ($5.5 less than $14), he would have gone to the Pastas.
So to summarise for my own edification to ensure the math works out:
An app is chosen with one of four prices (8.5, 12.5, 14, 20)
Based on which app price is chosen (highest to lowest), he picks the corresponding group of three prices:
Bread (4.5, 8.5, 10.5) [+20]
Soup (10.5, 14.5, 16.5) [+14]
Salad (12, 16, 18) [+12.5]
Pasta (16, 20, 22) [+8.5]
Total is always 24.5, 28.5 or 30.5 depending on if they picked the lowest, middle or highest price of the second group. He then picks the right entree group for the total he has at this point:
Mains (26, 34) [+30.5]
Specials (28?, 36) [+28.5]
Meats (32, 40) [+24.5]
Total is always either 56.5 or 64.5 depending on if they picked the lower or higher price of the entree group. I note that I am presuming that there is probably a special priced at $28 for the consistency of the trick, though it could be all specials of $36, and there is no second option if that group comes up. Same for Dessert:
Desserts (6.5, 10.5) [+64.5]
Cakes (14.5, 18.5) [+56.5]
Total is always either $71 or $75 based on which lower/higher price again.
Then he just picks the correct drink group (all priced the same) to finish the trick. $12 Wines if the total was $71, or $8 Aperitifs if it was $75.
The key is memorising all of the combos that make $83.00.