Is this why I don't like eating pizza while playing chess?
Fermat's Last Pizza
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THE FORMATING DOES NOT WORK WELL ON THIS LIST BELOW, BUT IT IS ARRANGED IN TYPES SEPARATED BY CATEGORIES AND SUB CATEGORIES.
chess squares 64 - chess pieces 32.
64 to the power of 32 = a number bigger than my calculator
i have listed the 542 most common normal pizza crusts - and 75 most normal pizza toppings. 542 to the power of 75 is a much larger number than than the number of chess positions! though the majority of possible chess positions are considered 'bad' every one of the possibilities i have listed for pizza are still edible and are options that have been sold in advertising restaurants.
red sauce, white sauce, garlic sauce, spicy sauce,
mozzarella, cheddar, jack, parmesan, provolone, blue, pepper jack, colby, swiss, feta, fontina, gorgonzola, ricotta, muenster, brick, gouda, asiago, gruyere, romano, processed(velvita/not real in my opinion, still used in pizza)
anchovies, shrimp, clams, oysters, salmon, squid, tuna, whitefish, lobster, crab
almonds, peanuts, pistachios, pecans, pinions, walnuts
bacon, bbq chicken, normal chicken, steak, ground beef, smoked ham, duck, honey ham, meatballs, pepperoni, sausage, salami, turkey, chorizo, prosciutto, canadian bacon,
basil, aflalfa sprouts, chilies, avocado, chives, leeks, cilantro, beets, coriander, blackbeans, cumin, broccoli, dill, capers, garlic, carrots, jalapeno, tomatoes, oregano, eggplant, rosemary, mushrooms, olives, bell pepper, onions, cauliflower, scallions, shallots, spinach, corn, watercress, cucumber, red pepper,
peanut butter, chocolate chips, cinnamon, marshmallows, gumdrops, m&ms, powdered sugar, candy worms, apple, pineapple,
crusts
tossed
personal
tray
cheese sprinkled
thin
stuffed
1. wheat
2. white
3. multi-grain
un-stuffed
4. wheat
5. white
6. multi-grain
thick
stuffed
7. wheat
8. white
9. multi-grain
un-stuffed
10. wheat
11. white
12. multigrain
non-cheese sprinkled
thin
stuffed
13. wheat
14. white
15. multi-grain
un-stuffed
16. wheat
17. white
18. multi-grain
thick
stuffed
19.. wheat
20. white
21. multi-grain
un-stuffed
22. wheat
23. white
24. multigrain
pan
deep
thin
stuffed
25. wheat
26. white
27. multi-grain
un-stuffed
28.. wheat
29. white
30. multi-grain
thick
stuffed
31. wheat
32. white
33. multi-grain
un-stuffed
34. wheat
35. white
36. multigrain
shallow
stuffed
37. wheat
38. white
39. multi-grain
un-stuffed
40. wheat
41. white
42. multi-grain
small
tray
cheese sprinkled
thin
stuffed
43. wheat
44. white
45. multi-grain
un-stuffed
46. wheat
47. white
48. multi-grain
thick
stuffed
49. wheat
50. white
51. multi-grain
un-stuffed
52. wheat
53. white
54. multigrain
non-cheese sprinkled
thin
stuffed
55. wheat
56. white
57. multi-grain
un-stuffed
58. wheat
59. white
60. multi-grain
thick
stuffed
61. wheat
62. white
63. multi-grain
un-stuffed
64. wheat
65. white
66. multigrain
pan
deep
thin
stuffed
67. wheat
68. white
69. multi-grain
un-stuffed
70. wheat
71. white
72. multi-grain
thick
stuffed
73. wheat
74. white
75. multi-grain
un-stuffed
76. wheat
77. white
78. multigrain
shallow
stuffed
79. wheat
80. white
81. multi-grain
un-stuffed
82. wheat
83. white
84. multi-grain
medium
tray
cheese sprinkled
thin
stuffed
85. wheat
86. white
87. multi-grain
un-stuffed
88. wheat
89. white
90. multi-grain
thick
stuffed
91. wheat
92. white
93. multi-grain
un-stuffed
94. wheat
95. white
96. multigrain
non-cheese sprinkled
thin
stuffed
97. wheat
98. white
99. multi-grain
un-stuffed
100. wheat
101. white
102. multi-grain
thick
stuffed
103. wheat
104. white
105. multi-grain
un-stuffed
106. wheat
107. white
108. multigrain
pan
deep
thin
stuffed
109. wheat
110. white
111. multi-grain
un-stuffed
112. wheat
113. white
114. multi-grain
thick
stuffed
115. wheat
116. white
117. multi-grain
un-stuffed
118. wheat
119. white
120. multigrain
shallow
stuffed
121. wheat
122. white
123. multi-grain
un-stuffed
124. wheat
125. white
126. multi-grain
large
tray
cheese sprinkled
thin
stuffed
127. wheat
128. white
129. multi-grain
un-stuffed
130. wheat
131. white
132. multi-grain
thick
stuffed
133. wheat
134. white
135. multi-grain
un-stuffed
136. wheat
137. white
138. multigrain
non-cheese sprinkled
thin
stuffed
139. wheat
140. white
141. multi-grain
un-stuffed
142. wheat
143. white
144. multi-grain
thick
stuffed
145. wheat
146. white
147. multi-grain
un-stuffed
148. wheat
149. white
150. multigrain
pan
deep
thin
stuffed
151. wheat
152. white
153. multi-grain
un-stuffed
154. wheat
155. white
156. multi-grain
thick
stuffed
157. wheat
158. white
159. multi-grain
un-stuffed
160. wheat
161. white
162. multigrain
shallow
stuffed
163. wheat
164. white
165. multi-grain
un-stuffed
167. wheat
168. white
169. multi-grain
extra-large
tray
cheese sprinkled
thin
stuffed
170. wheat
171. white
172. multi-grain
un-stuffed
173. wheat
174. white
175. multi-grain
thick
stuffed
176. wheat
177. white
178. multi-grain
un-stuffed
179. wheat
180. white
181. multigrain
non-cheese sprinkled
thin
stuffed
182. wheat
183. white
184. multi-grain
un-stuffed
185. wheat
186. white
187. multi-grain
thick
stuffed
188. wheat
189. white
190. multi-grain
un-stuffed
191. wheat
192. white
193. multigrain
pan
deep
thin
stuffed
194. wheat
195. white
196. multi-grain
un-stuffed
197. wheat
198. white
199. multi-grain
thick
stuffed
200. wheat
201. white
202. multi-grain
un-stuffed
203. wheat
204. white
205. multigrain
shallow
stuffed
206. wheat
207. white
208. multi-grain
un-stuffed
209. wheat
210. white
213. multi-grain
square -tray
cheese sprinkled
thin
stuffed
214. wheat
215. white
216. multi-grain
un-stuffed
217. wheat
218. white
219. multi-grain
thick
stuffed
220. wheat
221. white
222. multi-grain
un-stuffed
223. wheat
224. white
225. multigrain
non-cheese sprinkled
thin
stuffed
226. wheat
227. white
228. multi-grain
un-stuffed
229. wheat
230. white
231. multi-grain
thick
stuffed
232. wheat
233. white
234. multi-grain
un-stuffed
235. wheat
236. white
237. multigrain
crispy
stuffed
238. wheat
239. white
240. multi-grain
un-stuffed
241. wheat
242. white
243. multigrain
party
cheese sprinkled
thin
stuffed
244. wheat
245. white
246. multi-grain
un-stuffed
247. wheat
248. white
249. multi-grain
thick
stuffed
250. wheat
251. white
252. multi-grain
un-stuffed
253. wheat
254. white
255. multigrain
non-cheese sprinkled
thin
stuffed
256. wheat
257. white
258. multi-grain
un-stuffed
259. wheat
260. white
261. multi-grain
thick
stuffed
262. wheat
263. white
264. multi-grain
un-stuffed
265. wheat
266. white
267. multigrain
crispy
stuffed
268. wheat
269. white
270. multi-grain
un-stuffed
271. wheat
272. white
273. multigrain
rolled
personal
tray
cheese sprinkled
thin
stuffed
274. wheat
275. white
276. multi-grain
un-stuffed
277. wheat
278. white
279. multi-grain
thick
stuffed
280. wheat
281. white
282. multi-grain
un-stuffed
283. wheat
284. white
285. multigrain
non-cheese sprinkled
thin
stuffed
286. wheat
287. white
288. multi-grain
un-stuffed
289. wheat
290. white
291. multi-grain
thick
stuffed
292. wheat
293. white
294. multi-grain
un-stuffed
295. wheat
296. white
297. multigrain
pan
deep
thin
stuffed
298. wheat
299. white
300. multi-grain
un-stuffed
301. wheat
302. white
303. multi-grain
thick
stuffed
304. wheat
305. white
306. multi-grain
un-stuffed
307. wheat
308. white
309. multigrain
shallow
stuffed
310. wheat
311. white
312. multi-grain
un-stuffed
313. wheat
314. white
315. multi-grain
small
tray
cheese sprinkled
thin
stuffed
316. wheat
317. white
318. multi-grain
un-stuffed
319. wheat
320. white
321. multi-grain
thick
stuffed
322. wheat
323. white
324. multi-grain
un-stuffed
325. wheat
326. white
327. multigrain
non-cheese sprinkled
thin
stuffed
328. wheat
329. white
330. multi-grain
un-stuffed
331. wheat
332. white
333. multi-grain
thick
stuffed
334. wheat
335. white
336. multi-grain
un-stuffed
337. wheat
338. white
339. multigrain
pan
deep
thin
stuffed
340. wheat
341. white
342. multi-grain
un-stuffed
343. wheat
344. white
345. multi-grain
thick
stuffed
346. wheat
347. white
348. multi-grain
un-stuffed
349. wheat
350. white
351. multigrain
shallow
stuffed
352. wheat
353. white
354. multi-grain
un-stuffed
355. wheat
356. white
357. multi-grain
medium
tray
cheese sprinkled
thin
stuffed
358. wheat
359. white
360. multi-grain
un-stuffed
361. wheat
362. white
363. multi-grain
thick
stuffed
364. wheat
365. white
366. multi-grain
un-stuffed
367. wheat
368. white
369. multigrain
non-cheese sprinkled
thin
stuffed
370. wheat
371. white
372. multi-grain
un-stuffed
373. wheat
374. white
375. multi-grain
thick
stuffed
376. wheat
377. white
378. multi-grain
un-stuffed
379. wheat
380. white
381. multigrain
pan
deep
thin
stuffed
382. wheat
383. white
384. multi-grain
un-stuffed
385. wheat
386. white
387. multi-grain
thick
stuffed
388. wheat
389. white
390. multi-grain
un-stuffed
391. wheat
392. white
393. multigrain
shallow
stuffed
394. wheat
395. white
396. multi-grain
un-stuffed
397. wheat
398. white
399. multi-grain
large
tray
cheese sprinkled
thin
stuffed
400. wheat
401. white
402. multi-grain
un-stuffed
403. wheat
404. white
405. multi-grain
thick
stuffed
406. wheat
407. white
408. multi-grain
un-stuffed
409. wheat
410. white
411. multigrain
non-cheese sprinkled
thin
stuffed
412. wheat
413. white
414. multi-grain
un-stuffed
415. wheat
416. white
417. multi-grain
thick
stuffed
418. wheat
419. white
420. multi-grain
un-stuffed
421. wheat
422. white
423. multigrain
pan
deep
thin
stuffed
424. wheat
425. white
426. multi-grain
un-stuffed
427. wheat
428. white
429. multi-grain
thick
stuffed
430. wheat
431. white
432. multi-grain
un-stuffed
433. wheat
434. white
435. multigrain
shallow
stuffed
436. wheat
437. white
438. multi-grain
un-stuffed
439. wheat
440. white
441. multi-grain
extra-large
tray
cheese sprinkled
thin
stuffed
442. wheat
443. white
444. multi-grain
un-stuffed
445. wheat
446. white
447. multi-grain
thick
stuffed
448. wheat
449. white
450. multi-grain
un-stuffed
451. wheat
452. white
453. multigrain
non-cheese sprinkled
thin
stuffed
452. wheat
453. white
454. multi-grain
un-stuffed
455. wheat
456. white
457. multi-grain
thick
stuffed
458. wheat
459. white
460. multi-grain
un-stuffed
461. wheat
462. white
463. multigrain
pan
deep
thin
stuffed
464. wheat
465. white
467. multi-grain
un-stuffed
468. wheat
469. white
470. multi-grain
thick
stuffed
471. wheat
472. white
473. multi-grain
un-stuffed
474. wheat
475. white
476. multigrain
shallow
stuffed
477. wheat
478. white
479. multi-grain
un-stuffed
480. wheat
481. white
482. multi-grain
square -tray
cheese sprinkled
thin
stuffed
483. wheat
484. white
485. multi-grain
un-stuffed
486. wheat
487. white
488. multi-grain
thick
stuffed
489. wheat
490. white
491. multi-grain
un-stuffed
492. wheat
493. white
494. multigrain
non-cheese sprinkled
thin
stuffed
495. wheat
496. white
497. multi-grain
un-stuffed
498. wheat
499. white
500. multi-grain
thick
stuffed
501. wheat
502. white
503. multi-grain
un-stuffed
504. wheat
505. white
506. multigrain
crispy
stuffed
507. wheat
508. white
509. multi-grain
un-stuffed
510. wheat
511. white
512. multigrain
party
cheese sprinkled
thin
stuffed
513. wheat
514. white
515. multi-grain
un-stuffed
516. wheat
517. white
518. multi-grain
thick
stuffed
519. wheat
520. white
521. multi-grain
un-stuffed
522. wheat
523. white
524. multigrain
non-cheese sprinkled
thin
stuffed
525. wheat
526. white
527. multi-grain
un-stuffed
528. wheat
529. white
530. multi-grain
thick
stuffed
531. wheat
532. white
533. multi-grain
un-stuffed
534. wheat
535. white
536. multigrain
crispy
stuffed
537. wheat
538. white
539. multi-grain
un-stuffed
540. wheat
541. white
542. multigrain
Feb 3, 2009
0
#44
pastoryoshi wrote:
THE FORMATTING DOES NOT WORK WELL ON THIS LIST BELOW, BUT IT IS ARRANGED IN TYPES SEPARATED BY CATEGORIES AND SUB CATEGORIES.
chess squares 64 - chess pieces 32.
64 to the power of 32
If we accept these two numbers, there are 32 possibilities on the first square, followed by 32 possibilities on the 2nd square, and so on up to the 64th square.
So, although 6432 = approx 1057
the total actually comes to 32 to the power 64.
3264 = approx 1096
Don't forget that you can also have no piece on a square - which would give us 33 possible 'pieces', leading to a total of 3364 = approx 1097
However, the 8 white pawns are indistinguishable from each other. The 8 black pawns similarly. That is why I used a figure of 13 uniquely different occupants of each square i.e. black king, black queen, black bishop, black knight, black rook, black pawn white king, white queen, white bishop, white knight, white rook, white pawn and NO PIECE. Hence the total 1364 = approx 1071
= a number bigger than my calculator
The internet contains big calculators, including this one (http://www.calculatorfreeonline.com/calculators/exponent.php) for exponents.
I have listed the 542 most common normal pizza crusts - and 75 most normal pizza toppings. 542 to the power of 75 is a much larger number than than the number of chess positions!
I'm not entirely convinced this calculation is accurate. If there are 542 different bases, they would normally be considered mutually exclusive, so you wouldn't combine them. A base is either thin or thick: it can't be both. On that basis, we would simply multiply the total number of topping possibilities by the 542, without introducing exponents. On the other hand, if some of the options CAN be combined e.g. Thin and Cheesy, Thick and Cheesy - then we would have a set of factors that would need to be multiplied together.
In handling toppings, if you have 75 different ingredients, then you would calculate the total toppings using either PERMUTATIONS or COMBINATIONS, both of which involve using FACTORIALS rather than EXPONENTS. This reduces the apparent customer choice a little.
though the majority of possible chess positions are considered 'bad' every one of the possibilities I have listed for pizza are still edible and are options that have been sold in advertising restaurants.
This is a fair point: some of the chess position would be 'illegal' whereas the worst the pizzas could be is 'bad' for you.
red sauce, white sauce, garlic sauce, spicy sauce, ...
A most comprehensive list of ingredients. Keep up the good work!
Jul 13, 2010
0
#45
WOW I read your list of ingredients and I have to say I've tried every one except peanutbutter! it's time for me to switch to cheeseburgers,I can't do peanutbutter on pizza.
Jul 14, 2010
0
#46
Sparkx wrote: WOW I read your list of ingredients and I have to say I've tried every one except peanutbutter! it's time for me to switch to cheeseburgers,I can't do peanutbutter on pizza.
What a hog! 
artfizz wrote:
Sparkx wrote: WOW I read your list of ingredients and I have to say I've tried every one except peanutbutter! it's time for me to switch to cheeseburgers,I can't do peanutbutter on pizza.
What a hog!
Is that on the list somewhere?
Aug 10, 2010
0
#48
Sparkx wrote: WOW I read your list of ingredients and I have to say I've tried every one except peanutbutter! it's time for me to switch to cheeseburgers,I can't do peanutbutter on pizza.
artfizz wrote: What a hog!
ivandh wrote: Is that on the list somewhere?
That does it! You're on my hog list now as well.
Aug 10, 2010
0
#49
kramakintews wrote: I complained to the pizza delivery guy about wasted space in the box, and he asked me, "What you want your pie are squared?"
It's fun havin' you 'round.
That joke gets funnier each time I read it (may have something to do with my bottle getting emptier).
Speaking of math jokes, why is a cylinder of radius z and thickness a tasty? Because its volume would be pi*z*z*a.
And with a little calculus, you can find its center of mass at x-bar and y-bar, both of which have some nice selections on draught.
What in the world
You´re all missing the basic point. As soon as a pizza comes out of the oven it starts to change, chemically and biologically. Anyone who has forgotten a pizza and gone on holiday has ample proof of this on his return. A pizza consists not only of ham, anchovies and whatever, but (from a certain temperature downwards) of myriads of bacteria, spores, fungi (without the "h") and possibly (depending on the (un-) hygienic habits of your delivery sevice) viruses. Even when colonised with millions of these life forms, a pizza is still recognizably and definably a pizza (Gertrude Stein: "a pizza is a pizza is a pizza" is an early draft of a very famous poem of hers). And therefore: even if it were possible to bake two (or billions of) absolutely identical pizzas; the permutations of colonization by microorganisms are truly infinite.
This is not true of chess pieces, positions or "games". Anderssen´s Immortal is always the same, whether displayed on Houdini, your 30 year old Atari, or demonstrated with Indian carved ivory pieces from the 15th century. Pizza wins hands down, QED.
Best pizza ever had was in an Italian village called ''Rapallo'' which is near ''Portofino, Santa Margherita, Ligune''.
Worth the air-fare & great place to vacation.
Sep 16, 2012
0
#56
Ben_Lui wrote:
You´re all missing the basic point. As soon as a pizza comes out of the oven it starts to change, chemically and biologically. Anyone who has forgotten a pizza and gone on holiday has ample proof of this on his return. A pizza consists not only of ham, anchovies and whatever, but (from a certain temperature downwards) of myriads of bacteria, spores, fungi (without the "h") and possibly (depending on the (un-) hygienic habits of your delivery sevice) viruses. Even when colonised with millions of these life forms, a pizza is still recognizably and definably a pizza (Gertrude Stein: "a pizza is a pizza is a pizza" is an early draft of a very famous poem of hers). And therefore: even if it were possible to bake two (or billions of) absolutely identical pizzas; the permutations of colonization by microorganisms are truly infinite.
This is not true of chess pieces, positions or "games". Anderssen´s Immortal is always the same, whether displayed on Houdini, your 30 year old Atari, or demonstrated with Indian carved ivory pieces from the 15th century. Pizza wins hands down, QED.
To be fair, we should compare chess positions and pizza toppings as logical entities rather than physical objects (in which case the pizza still wins comfortably). At the the physical level, we would have to include the virii and bacteria not only on the pizza but also on the chess pieces (from unhygenic players).
You are restricting the number of possibilities unnecessarily by insisting on drawing your possible toppings from the set of rational toppings between 0oz and 1oz.
I was proposing restricting it to integers in range 1 .. 64 - which is quite a bit smaller than the intervals you suggest. Using 'real' ingredients would certainly allow more variants - though your palate would need to be keen to detect the differences.
Pizza analysis shows that you can have an infinite number of toppings if you add in the set of irrational toppings over that interval thus producing the real topping set on the interval [0,1]. I have made the interval closed since it is possible to order a pizza with no topping at all (that is a base for the pizza space) and one with exactly enough topping to complete the pizza (whether square or round).
Some pizza toppings seem irrational already. Allowing the genuinely irrational would extend the range - but increase the complexity for the cook.
Part of the difficulty, though, arises from comparing a count of physical objects (pizza toppings) with a count of logical objects (chess positions). Since no two physical objects are identical, we could simply restrict ourselves to ham and pineapple pizzas; a very large number is possible since each one is likely to differ from all others by at least one molecule.
The next question is "How big is the infinite set of real toppings?" How about if we allow complex toppings as solutions so that we can produce quadratic pizzas?
All these numbers are making me hungry. Does anyone feel like a pizza? Which topping would you like?