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Under Pressure

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Part 1: Evaluate each of the following equations.

EXAMPLE = x_1 + x_2 - x_3\[EXAMPLE = x_1 + x_2 - x_3\] where:

  • x_1 =\(x_1 =\) "___, play Despacito" (meme referring to an Amazon product);|x_1| = 5\(|x_1| = 5\)
  • x_2 =\(x_2 =\) Random subset, or free Costco treat; |x_2| = 6\(|x_2| = 6\)
  • x_3 =\(x_3 =\) Interjection denoting grief or sorrow; |x_3| = 4\(|x_3| = 4\)

DEMONSTRATION = x_1 + x_2 \cdot x_3 - 501\[DEMONSTRATION = x_1 + x_2 \cdot x_3 - 501\] where:

  • x_1 =\(x_1 =\) Angels & ___ (Dan Brown novel); |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) Characteristic; |x_2| = 5\(|x_2| = 5\)
  • x_3 =\(x_3 =\) "My Heart Will Go On" singer; |x_3| = 4\(|x_3| = 4\)

[8 points] y_1=\frac{\sqrt{i\cdot(x_1^2 - \lim x_2) + x_3 + \frac{x_4}{2}}}{x_5}\[y_1=\frac{\sqrt{i\cdot(x_1^2 - \lim x_2) + x_3 + \frac{x_4}{2}}}{x_5}\] where:

  • x_1 =\(x_1 =\) ___ Alto (birthplace of Hewlett-Packard); |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Company formerly known as X.com; |x_2| = 6\(|x_2| = 6\)
  • x_3 =\(x_3 =\) You, currently, vis-a-vis this puzzle; |x_3| = 6\(|x_3| = 6\)
  • x_4 =\(x_4 =\) "My ___ is too big" (internet meme along with "I am a banana"); |x_4| = 5\(|x_4| = 5\)
  • x_5 =\(x_5 =\) LoL champion who attacks with an anchor; |x_5| = 8\(|x_5| = 8\)

[6 points] y_2 = \int (\sqrt{(x_1 - 51 + 2000)^2} - x_2 )\cdot dS\[y_2 = \int \left(\sqrt{(x_1 - 51 + 2000)^2} - x_2 \right)\cdot dS\] where:

  • x_1 =\(x_1 =\) Indonesian island known for honeymooning; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Famous pirate captain from Treasure Island; |x_2| = 5\(|x_2| = 5\)

[7 points] y_3 = \nabla \cdot (\lim (x_1 + \frac{x_2}{x_3})) + \frac{x_4}{2} - x_5\[y_3 = \nabla \cdot \left(\lim \left(x_1 + \frac{x_2}{x_3}\right)\right) + \frac{x_4}{2} - x_5\] where:

  • x_1 =\(x_1 =\) Bad-tempered, cantankerous; |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) Type of sea creature that eats Mr Krabs' millionth dollar; |x_2| = 4\(|x_2| = 4\)
  • x_3 =\(x_3 =\) Door, or snippet in a log; |x_3| = 5\(|x_3| = 5\)
  • x_4 =\(x_4 =\) Movie aka "The Bus That Couldn't Slow Down"; |x_4| = 5\(|x_4| = 5\)
  • x_5 =\(x_5 =\) Highschool dance; |x_5| = 4\(|x_5| = 4\)

[9 points] y_4 = (\nabla \cdot (x_1 + x_2 - 50)) - x_3 + \frac{d}{dT}(x_4)\[y_4 = (\nabla \cdot (x_1 + x_2 - 50)) - x_3 + \frac{d}{dT}(x_4)\] where:

  • x_1 =\(x_1 =\) Implement for untangling hair; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Had a strong carnal desire for; |x_2| = 6\(|x_2| = 6\)
  • x_3 =\(x_3 =\) Swore at, with "out"; |x_3| = 6\(|x_3| = 6\)
  • x_4 =\(x_4 =\) Manner in which something is arranged, such as an HTML page; |x_4| = 6\(|x_4| = 6\)

[7 points] y_5 = \int i \cdot ((x_1 - x_2) + (x_3 - i \cdot x_4)) \cdot dP\[y_5 = \int i \cdot ((x_1 - x_2) + (x_3 - i \cdot x_4)) \cdot dP\] where:

  • x_1 =\(x_1 =\) Dead bird in a Monty Python sketch; |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) It can be modern or abstract; |x_2| = 3\(|x_2| = 3\)
  • x_3 =\(x_3 =\) Give up, as a game; |x_3| = 7\(|x_3| = 7\)
  • x_4 = |x_4|\(x_4 = |x_4|\), as an English word

[7 points] y_6 = x_1 \cdot x_2 + (-\frac{d}{dQ}(x_3)) - (x_4 - 500)\[y_6 = x_1 \cdot x_2 + \left(-\frac{d}{dQ}(x_3)\right) - (x_4 - 500)\] where:

  • x_1 =\(x_1 =\) State or assert formally; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Insult, as in some rap tracks; |x_2| = 4\(|x_2| = 4\)
  • x_3 =\(x_3 =\) Word following "Bugs" or "Playboy"; |x_3| = 5\(|x_3| = 5\)
  • x_4 =\(x_4 =\) Harmful or obstructive, like weather conditions; |x_4| = 7\(|x_4| = 7\)

[9 points] y_7 = \nabla \times \sqrt{x_1 - (x_2 - x_3)} + x_4 - x_5\[y_7 = \nabla \times \sqrt{x_1 - (x_2 - x_3)} + x_4 - x_5\] where:

  • x_1 =\(x_1 =\) Padme's surname; |x_1| = 7\(|x_1| = 7\)
  • x_2 =\(x_2 =\) Having tender feelings, emotional; |x_2| = 11\(|x_2| = 11\)
  • x_3 =\(x_3 =\) Conscious; |x_3| = 8\(|x_3| = 8\)
  • x_4 =\(x_4 =\) Supergiant Games RPC featuring "The Kid"; |x_4| = 7\(|x_4| = 7\)
  • x_5 =\(x_5 =\) Word with which Laszlo transforms; |x_5| = 3\(|x_5| = 3\)

[10 points] y_8 = (-e^{x_1}) + \frac{x_2}{2} + \frac{i\cdot x_3}{3}\[y_8 = (-e^{x_1}) + \frac{x_2}{2} + \frac{i\cdot x_3}{3}\] where:

  • x_1 =\(x_1 =\) Sagacious, showing good judgment; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Mystery ___ Theater 3000; |x_2| = 7\(|x_2| = 7\)
  • x_3 =\(x_3 =\) Redact or bleep; |x_3| = 6\(|x_3| = 6\)

[8 points] y_9 = \int \frac{x_1}{\nabla \cdot(x_2 - x_3)} \cdot dT + x_4 - x_5\[y_9 = \int \frac{x_1}{\nabla \cdot(x_2 - x_3)} \cdot dT + x_4 - x_5\] where:

  • x_1 =\(x_1 =\) "Ol' Blue Eyes"; |x_1| = 7\(|x_1| = 7\)
  • x_2 =\(x_2 =\) Marshes, swamps, etc.; |x_2| = 8\(|x_2| = 8\)
  • x_3 =\(x_3 =\) Light brown; |x_3| = 3\(|x_3| = 3\)
  • x_4 =\(x_4 =\) Outdoor elevated platform attached to a building; |x_4| = 7\(|x_4| = 7\)
  • x_5 =\(x_5 =\) "Push button, receive ___" (misinterpreted instructions on an automatic hand dryer); |x_5| = 5\(|x_5| = 5\)

[10 points] y_{10} = (\int x_1 \cdot dB) + i \cdot \frac{d}{dT}(e^{x_2 - 1})\[y_{10} = \left(\int x_1 \cdot dB\right) + i \cdot \frac{d}{dT}(e^{x_2 - 1})\] where:

  • x_1 =\(x_1 =\) Most courageous; |x_1| = 7\(|x_1| = 7\)
  • x_2 =\(x_2 =\) Long reclining chair, or "chair" in French; |x_2| = 6\(|x_2| = 6\)

[10 points] y_{11} = \nabla \times (\sqrt{x_1 - x_2} - x_3) + \int x_4 \cdot dL\[y_{11} = \nabla \times (\sqrt{x_1 - x_2} - x_3) + \int x_4 \cdot dL\] where:

  • x_1 =\(x_1 =\) Parents, grandparents, etc.; |x_1| = 9\(|x_1| = 9\)
  • x_2 =\(x_2 =\) Star or extra; |x_2| = 5\(|x_2| = 5\)
  • x_3 =\(x_3 =\) Tied, or maximum; |x_3| = 5\(|x_3| = 5\)
  • x_4 =\(x_4 =\) Dismal, like an outlook; |x_4| = 5\(|x_4| = 5\)

[6 points] y_{12} = \frac{x_1}{x_2 \cdot x_3}\[y_{12} = \frac{x_1}{x_2 \cdot x_3}\] where:

  • x_1 =\(x_1 =\) Shuriken wielder; |x_1| = 5\(|x_1| = 5\)
  • x_2 =\(x_2 =\) Abu Dhabi country (abbr.); |x_2| = 3\(|x_2| = 3\)
  • x_3 =\(x_3 =\) Gave, as a wish or a monetary endorsement; |x_3| = 7\(|x_3| = 7\)

[8 points] y_{13} = \oint(x_1 + (x_2^2 - (-e^{x_3}))) \cdot dL\[y_{13} = \oint\left(x_1 + \left(x_2^2 - (-e^{x_3})\right)\right) \cdot dL\] where:

  • x_1 =\(x_1 =\) William of legend; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Blue hue or bird; |x_2| = 4\(|x_2| = 4\)
  • x_3 =\(x_3 =\) Fiesta or political group; |x_3| = 5\(|x_3| = 5\)

[8 points] y_{14} = ((\oint (x_1 \cdot dA) - \lim x_2)^2 - 1 - x_3 ) \cdot (i \cdot x_4)\[y_{14} = \left(\left(\oint (x_1 \cdot dA) - \lim x_2\right)^2 - 1 - x_3 \right) \cdot (i \cdot x_4)\] where:

  • x_1 =\(x_1 =\) Debilitating headaches that often come with auras; |x_1| = 9\(|x_1| = 9\)
  • x_2 =\(x_2 =\) Octagonal outdoor pavilions; |x_2| = 7\(|x_2| = 7\)
  • x_3 =\(x_3 =\) Opposite of max; |x_3| = 3\(|x_3| = 3\)
  • x_4 =\(x_4 =\) Put words down on paper; |x_4| = 5\(|x_4| = 5\)

[9 points] y_{15} = \oint \lim(x_1 + (i \cdot (x_2 + x_3 + (x_4 - x_5))) \cdot dZ\[y_{15} = \oint \lim(x_1 + (i \cdot (x_2 + x_3 + (x_4 - x_5))) \cdot dZ\] where:

  • x_1 =\(x_1 =\) City containing the Black Stone; |x_1| = 5\(|x_1| = 5\)
  • x_2 =\(x_2 =\) Netflix thriller about serial killer Joe; |x_2| = 3\(|x_2| = 3\)
  • x_3 =\(x_3 =\) ___ mints (arguably the best kind of Girl Scout cookie); |x_3| = 4\(|x_3| = 4\)
  • x_4 =\(x_4 =\) Main presentations at conferences; |x_4| = 8\(|x_4| = 8\)
  • x_5 =\(x_5 =\) Square, clove, or slip; |x_5| = 4\(|x_5| = 4\)

[7 points] y_{16} = x_1 \cdot ( e^{\nabla \times (x_2 + \frac{x_3}{3})} - 1000)\[y_{16} = x_1 \cdot \left( e^{\nabla \times \left(x_2 + \frac{x_3}{3}\right)} - 1000\right)\] where:

  • x_1 =\(x_1 =\) Heap; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Say haha, chortle; |x_2| = 5\(|x_2| = 5\)
  • x_3 =\(x_3 =\) Sequence of data points sorted in chronological order; |x_3| = (4, 6)\(|x_3| = (4, 6)\)

[8 points] y_{17} = (-x_1) + e^{\oint x_2 \cdot dE} - 1000\[y_{17} = (-x_1) + e^{\oint x_2 \cdot dE} - 1000\] where:

  • x_1 =\(x_1 =\) One who did the crime, in cop talk; |x_1| = 4\(|x_1| = 4\)
  • x_2 =\(x_2 =\) Flavor or preference; |x_2| = 5\(|x_2| = 5\)

[8 points] y_{18} = \int \sqrt{i \cdot x_1} \cdot (\nabla \times (\frac{d}{dO}(i \cdot x_2))) \cdot dO\[y_{18} = \int \sqrt{i \cdot x_1} \cdot \left(\nabla \times \left(\frac{d}{dO}(i \cdot x_2)\right)\right) \cdot dO\] where:

  • x_1 =\(x_1 =\) Person grabbing or confiscating something; |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) 24-hour periods; |x_2| = 4\(|x_2| = 4\)

[10 points] y_{19} = \nabla \cdot x_1 + (x_2 - \frac{\lim(x_3 + x_4)}{2})\[y_{19} = \nabla \cdot x_1 + \left(x_2 - \frac{\lim(x_3 + x_4)}{2}\right)\] where:

  • x_1 =\(x_1 =\) VP under Bush; |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) Ought not to; |x_2| = 8\(|x_2| = 8\)
  • x_3 =\(x_3 =\) "Great ___!" (Doc Brown catchphrase); |x_3| = 5\(|x_3| = 5\)
  • x_4 =\(x_4 =\) Moved on one's hands and knees; |x_4| = 7\(|x_4| = 7\)

[8 points] y_{20} = \frac{i \cdot (-x_1 + e^{x_2})}{x_3 \cdot x_4}\[y_{20} = \frac{i \cdot (-x_1 + e^{x_2})}{x_3 \cdot x_4}\] where:

  • x_1 =\(x_1 =\) Computer memory or sheep; |x_1| = 3\(|x_1| = 3\)
  • x_2 =\(x_2 =\) It costs 2 grain and 3 ore; |x_2| = 4\(|x_2| = 4\)
  • x_3 =\(x_3 =\) Underlying essence, or bit of code shared on GitHub; |x_3| = 4\(|x_3| = 4\)
  • x_4 =\(x_4 =\) Torvalds of Linux fame; |x_4| = 5\(|x_4| = 5\)

[6 points] y_{21} = (x_1 - i \cdot e^{\frac{x_2}{x_3}}) \cdot x_4\[y_{21} = \left(x_1 - i \cdot e^{\frac{x_2}{x_3}}\right) \cdot x_4\] where:

  • x_1 =\(x_1 =\) ___ horse (painful cramp) ; |x_1| = 7\(|x_1| = 7\)
  • x_2 =\(x_2 =\) National dish of South Korea; |x_2| = 6\(|x_2| = 6\)
  • x_3 =\(x_3 =\) Young newt ; |x_3| = 3\(|x_3| = 3\)
  • x_4 =\(x_4 =\) Class of minivan-like car that doesn't really have much to do with athletics (acronym); |x_4| = 3\(|x_4| = 3\)

[8 points] y_{22} = 50 \cdot (x_1 + (\nabla \times x_2 - 501) - (x_3 \cdot \frac{d}{dK}(\nabla \times x_4) - \int x_5 \cdot dH))\[y_{22} = 50 \cdot \left(x_1 + (\nabla \times x_2 - 501) - \left(x_3 \cdot \frac{d}{dK}(\nabla \times x_4) - \int x_5 \cdot dH\right)\right)\] where:

  • x_1 =\(x_1 =\) Actress Sissy of Homecoming; |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) Actress Bergman; |x_2| = 6\(|x_2| = 6\)
  • x_3 =\(x_3 =\) Flower from the Greek for "star"; |x_3| = 5\(|x_3| = 5\)
  • x_4 =\(x_4 =\) One of 435 in the House of Representatives; |x_4| = 4\(|x_4| = 4\)
  • x_5 =\(x_5 =\) Whipped, as with a belt; |x_5| = 6\(|x_5| = 6\)

[9 points] y_{23} = (x_1 - \sqrt{\nabla \cdot (x_2 + x_3)}) \cdot \frac{x_4}{x_5}\[y_{23} = (x_1 - \sqrt{\nabla \cdot (x_2 + x_3)}) \cdot \frac{x_4}{x_5}\] where:

  • x_1 =\(x_1 =\) Ron Swanson's just says "I can do what I want"; |x_1| = 6\(|x_1| = 6\)
  • x_2 =\(x_2 =\) State flower of Indiana; |x_2| = 5\(|x_2| = 5\)
  • x_3 =\(x_3 =\) Copper current conductor; |x_3| = 4\(|x_3| = 4\)
  • x_4 =\(x_4 =\) Dance or taco condiment; |x_4| = 5\(|x_4| = 5\)
  • x_5 =\(x_5 =\) 0, ±1, ±2, … ; |x_5| = 8\(|x_5| = 8\)

Check your answers:

  • 2nd-level wizard spell
  • Amusement
  • Anguish
  • Apes etc.
  • Being lazy
  • Bendy
  • Bewilderment
  • Car or cat
  • Fabled sailor
  • Fatigue
  • Fresh-tasting flavor
  • Gets rid of, as rumors
  • Holy
  • Lack of C on the high seas
  • Like a rough voice
  • Lower level
  • Made reparations
  • Ready
  • Sight in many churchyards
  • Soak in seasoning
  • This event, for one
  • Traitor
  • Type of needlework

Part 2: Proofs

Problem 1: Prove Theorem T_1\(T_1\) given
y_{12,2} y_{13,1} y_{11,10} y_{9,3} y_{23,1} y_{6,5} y_{22,2} y_{18,6} y_{19,4} y_{2,5} y_{17,2} (hyph)\[y_{12,2} y_{13,1} y_{11,10} y_{9,3} y_{23,1} y_{6,5} y_{22,2} y_{18,6} y_{19,4} y_{2,5} y_{17,2}\,(hyph)\]
y_{4,4} y_{20,3} y_{15,4} y_{19,3}\[y_{4,4} y_{20,3} y_{15,4} y_{19,3}\]
y_{16,1} y_{3,2} y_{8,3} y_{23,2}\[y_{16,1} y_{3,2} y_{8,3} y_{23,2}\]

Problem 2: Prove Theorem T_2\(T_2\) given
y_{14,6} y_{7,9} y_{1,3} y_{20,5} y_{10,5}\[y_{14,6} y_{7,9} y_{1,3} y_{20,5} y_{10,5}\]
y_{21,2} y_{11,9} y_{8,6} y_{5,2} y_{10,9}\[y_{21,2} y_{11,9} y_{8,6} y_{5,2} y_{10,9}\]
y_{4,1} y_{15,5} y_{7,5} y_{1,5} y_{22,3} y_{9,1} y_{14,8}\[y_{4,1} y_{15,5} y_{7,5} y_{1,5} y_{22,3} y_{9,1} y_{14,8}\]

Problem 3: Prove Theorem T_3\(T_3\) given
y_{3,1} y_{18,7} y_{16,6} y_{13,6} y_{21,6} y_{17,7} y_{6,1}\[y_{3,1} y_{18,7} y_{16,6} y_{13,6} y_{21,6} y_{17,7} y_{6,1}\]
y_{19,5} y_{5,6} y_{2,6}\[y_{19,5} y_{5,6} y_{2,6}\]
y_{8,4} y_{12,5} y_{10,2} y_{11,4} y_{7,4} y_{17,8}\[y_{8,4} y_{12,5} y_{10,2} y_{11,4} y_{7,4} y_{17,8}\]

by applying the "Rhythm" lemma, "Overdue" lemma, "Tie" lemma, and "Shield or division" lemma.

Problem 4: Prove Theorem T_4\(T_4\) given
y_{22,4} y_{23,7} y_{13,3} y_{15,2} y_{14,7} y_{4,6}\[y_{22,4} y_{23,7} y_{13,3} y_{15,2} y_{14,7} y_{4,6}\]
y_{20,4} y_{18,3} y_{1,2} y_{9,5} y_{8,7} y_{3,4}\[y_{20,4} y_{18,3} y_{1,2} y_{9,5} y_{8,7} y_{3,4}\]

by equating both sides to "Most serious" and using the "Dispossess" lemma.

N.B.: This result has several versions of differing length, please use the uncapitalized version.

Problem 5: Prove Theorem T_5\(T_5\) given
y_{5,4} y_{10,8} y_{19,7} y_{7,8}\[y_{5,4} y_{10,8} y_{19,7} y_{7,8}\]
y_{16,3} y_{15,6} y_{11,5} y_{23,3} y_{12,3} y_{21,4} y_{2,1} y_{4,9} y_{8,1} y_{6,3}\[y_{16,3} y_{15,6} y_{11,5} y_{23,3} y_{12,3} y_{21,4} y_{2,1} y_{4,9} y_{8,1} y_{6,3}\]
y_{9,7} y_{14,2} y_{18,4} y_{20,6} y_{22,7} y_{17,5} y_{13,5} y_{19,6}\[y_{9,7} y_{14,2} y_{18,4} y_{20,6} y_{22,7} y_{17,5} y_{13,5} y_{19,6}\]
y_{20,1} y_{15,7} y_{23,8} y_{10,1}\[y_{20,1} y_{15,7} y_{23,8} y_{10,1}\]

by equating both sides to "Ritz" and using the "Radio butt." lemma, "Sparkle" lemma, "Tennis sweep" lemma, and "Leer" lemma.

Problem 6: Prove Theorem T_6\(T_6\) given
y_{11,1} y_{1,6} y_{15,3} y_{9,8}\[y_{11,1} y_{1,6} y_{15,3} y_{9,8}\]
y_{5,7} y_{4,5} y_{16,5} y_{3,5}\[y_{5,7} y_{4,5} y_{16,5} y_{3,5}\]

by equating both sides to "Ticket remainder" and using the "No ifs, ands, or what" lemma.

Problem 7: Prove Theorem T_7\(T_7\) given
y_{14,1} y_{18,5} y_{19,1} y_{7,6}\[y_{14,1} y_{18,5} y_{19,1} y_{7,6}\]
y_{21,1} y_{11,3} y_{1,8} y_{8,8}\[y_{21,1} y_{11,3} y_{1,8} y_{8,8}\]
y_{10,4} y_{13,4} y_{7,1}\[y_{10,4} y_{13,4} y_{7,1}\]
y_{9,4} y_{2,3} y_{6,2} y_{3,7}\[y_{9,4} y_{2,3} y_{6,2} y_{3,7}\]

using the "Palindromic scifi character" lemma, "Meat" lemma, "Journey" lemma, and "Bright" lemma.

Hint: As a first step, multiply by a constant and compare to a positive integer power.

Problem 8: Prove Theorem T_8\(T_8\) given
y_{4,2} y_{7,3} y_{17,3} y_{19,9} y_{12,6} y_{23,4} y_{5,1} y_{22,5} (2 words)\[y_{4,2} y_{7,3} y_{17,3} y_{19,9} y_{12,6} y_{23,4} y_{5,1} y_{22,5}\,(2\,words)\]
y_{18,1} y_{16,4} y_{8,10} y_{10,6} y_{1,4} y_{21,5} y_{11,8} y_{17,6}\[y_{18,1} y_{16,4} y_{8,10} y_{10,6} y_{1,4} y_{21,5} y_{11,8} y_{17,6}\]

by equating both sides to "Bring too much" and applying the "Bridge" lemma.

Check your answers: |T| = \{(4, 6, 7, 7, 8, 9, 10, 11)\}\[|T| = \{(4, 6, 7, 7, 8, 9, 10, 11)\}\], omitting possessive S's.

ANS = T_{2,3} T_{3,7} T_{1,9} T_{7,6} T_{8,2} T_{4,4} T_{6,5} T_{7,1} T_{3,3} T_{5,7} T_{1,3} T_{2,2} T_{5,3} T_{4,8} T_{3,1} T_{8,3} T_{7,5} T_{1,2} T_{3,2} T_{7,2} T_{4,5} T_{5,6} T_{8,5} T_{7,3} T_{6,1} T_{8,1} T_{5,2} T_{6,2} T_{1,11} T_{4,1} T_{6,6} T_{3,6}\[ANS = T_{2,3} T_{3,7} T_{1,9} T_{7,6} T_{8,2} T_{4,4} T_{6,5} T_{7,1} T_{3,3} T_{5,7} T_{1,3} T_{2,2} T_{5,3} T_{4,8} T_{3,1} T_{8,3} T_{7,5} T_{1,2} T_{3,2} T_{7,2} T_{4,5} T_{5,6} T_{8,5} T_{7,3} T_{6,1} T_{8,1} T_{5,2} T_{6,2} T_{1,11} T_{4,1} T_{6,6} T_{3,6}\]