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PUZZLE POTLUCK 3

Solution – Stoichiometry 101
ANSWER – SYNTHESIS
by Julz Huang and Stephanie Chang

1 Dimensional Analysis

Part 1 contains several scenarios which each require finding a coefficient to express each answer in terms of the previous answer. Let us denote our coefficients as a, b, ... o, where A = a ⋅\cdot O, etc. Then, the coefficients are as follows:

1. How many tanks does he use up in O hours?

a = 3600 s1 hr⋅299792458 m1 s⋅1 Gm1000000000 m⋅1 tank1435 Gm=1541789784 tanks2050000000 hr≈\frac{3600 \text{ s}}{1 \text{ hr}} \cdot \frac{299792458 \text{ m}}{1 \text{ s}} \cdot \frac{1 \text{ Gm}}{1000000000 \text{ m}} \cdot \frac{1 \text{ tank}}{1435 \text{ Gm}} = \frac{1541789784 \text{ tanks}}{2050000000 \text{ hr}} \approx 0.752092578

A = 0.752092578 ⋅\cdot O

2. How many NBA basketball court lengths does the ball travel from Kobe’s passes in A games?

b = 4 quarters1 game⋅3 passes1 quarter⋅62.7 in1 pass⋅1 ft12 in⋅1 court length94 ft=627 court lengths940 games≈\frac{4 \text{ quarters}}{1 \text{ game}} \cdot \frac{3 \text{ passes}}{1 \text{ quarter}} \cdot \frac{62.7 \text{ in}}{1 \text{ pass}} \cdot \frac{1 \text{ ft}}{12 \text{ in}} \cdot \frac{1 \text{ court length}}{94 \text{ ft}} = \frac{627 \text{ court lengths}}{940 \text{ games}} \approx 0.667021277

B = 0.667021277 ⋅\cdot A

3. How many Dark Arts rank progress bars can he fill in B minutes?

c = 1 potion brewed(120⋅0.58) min⋅243 battles25 potions brewed⋅10 points1 battle⋅1 bar100 points=81 bars5800 min≈\frac{1 \text{ potion brewed}}{(120 \cdot 0.58) \text{ min}} \cdot \frac{243 \text{ battles}}{25 \text{ potions brewed}} \cdot \frac{10 \text{ points}}{1 \text{ battle}} \cdot \frac{1 \text{ bar}}{100 \text{ points}} = \frac{81 \text{ bars}}{5800 \text{ min}} \approx 0.0139655172

C = 0.0139655172 ⋅\cdot B

4. How many bottles does Julz go through in C days?

d = 1440 min1 day⋅106 beats1 min⋅1 dance1314 beats⋅5 shots2 dances⋅1 bottle16 shots=1325 bottles73 days≈\frac{1440 \text{ min}}{1 \text{ day}} \cdot \frac{106 \text{ beats}}{1 \text{ min}} \cdot \frac{1 \text{ dance}}{1314 \text{ beats}} \cdot \frac{5 \text{ shots}}{2 \text{ dances}} \cdot \frac{1 \text{ bottle}}{16 \text{ shots}} = \frac{1325 \text{ bottles}}{73 \text{ days}} \approx 18.1506849

D = 18.1506849 ⋅\cdot C

5. How many US fluid barrels of seawater do they intake?

e = 3600 sec1 hr⋅1 wave13 sec⋅21 strokes1 wave⋅3 sips1 stroke⋅1 cup59 sips⋅1 barrel504 cups=450 barrels767 hr≈\frac{3600 \text{ sec}}{1 \text{ hr}} \cdot \frac{1 \text{ wave}}{13 \text{ sec}} \cdot \frac{21 \text{ strokes}}{1 \text{ wave}} \cdot \frac{3 \text{ sips}}{1 \text{ stroke}} \cdot \frac{1 \text{ cup}}{59 \text{ sips}} \cdot \frac{1 \text{ barrel}}{504 \text{ cups}} = \frac{450 \text{ barrels}}{767 \text{ hr}} \approx 0.586701434

E = 0.586701434 ⋅\cdot D

6. This is the number of Dr. Seuss books equivalent to the number of words she wrote during all Final Jeopardy! rounds.

f = 4 words1 Final Jeopardy! round⋅1 books1270 words=2 books635 Final Jeopardy! rounds≈\frac{4 \text{ words}}{1 \text{ Final Jeopardy! round}} \cdot \frac{1 \text{ books}}{1270 \text{ words}} = \frac{2 \text{ books}}{635 \text{ Final Jeopardy! rounds}} \approx 0.00314960630

F = 0.00314960630 ⋅\cdot (E + 1)

7. How many pizzas worth of calories are expended if (F*100)% of the city population of 600,000 attempt the course?

g = 16 calories1 run⋅1 slice219 calories⋅1 pizza8 slices⋅600000 people=1200000 pizzas219 runs≈\frac{16 \text{ calories}}{1 \text{ run}} \cdot \frac{1 \text{ slice}}{219 \text{ calories}} \cdot \frac{1 \text{ pizza}}{8 \text{ slices}} \cdot 600000 \text{ people} = \frac{1200000 \text{ pizzas}}{219 \text{ runs}} \approx 5479.45205

G = 5479.45205 ⋅\cdot F

8. How many Fitbit Adventures does Bruce go through in G runs of the Superman ride?

h = 100 steps1 ride⋅1 Fitbit Adventure38000 steps=1 Fitbit Adventure380 rides≈\frac{100 \text{ steps}}{1 \text{ ride}} \cdot \frac{1 \text{ Fitbit Adventure}}{38000 \text{ steps}} = \frac{1 \text{ Fitbit Adventure}}{380 \text{ rides}} \approx 0.00263157895

H = 0.00263157895 ⋅\cdot G

9. How many albums are corrupted on one computer after H days? i = 400 MB1 day⋅1 file6 MB⋅1 album11 files=200 albums33 days≈\frac{400 \text{ MB}}{1 \text{ day}} \cdot \frac{1 \text{ file}}{6 \text{ MB}} \cdot \frac{1 \text{ album}}{11 \text{ files}} = \frac{200 \text{ albums}}{33 \text{ days}} \approx 6.06060606

I = 6.06060606 ⋅\cdot H

10. How many skeins of yarns does she go through? j = 1 scarf10 hr⋅138 rows1 scarf⋅18 stitches1 row⋅1 skein282 stitches=414 skeins470 hr≈\frac{1 \text{ scarf}}{10 \text{ hr}} \cdot \frac{138 \text{ rows}}{1 \text{ scarf}} \cdot \frac{18 \text{ stitches}}{1 \text{ row}} \cdot \frac{1 \text{ skein}}{282 \text{ stitches}} = \frac{414 \text{ skeins}}{470 \text{ hr}} \approx 0.880851064

J = 0.880851064 ⋅\cdot I

11. How many forests does Lancelot need to harvest to complete matches in a J-week season?

k = 1 fortnight2 weeks⋅1 match1 fortnight⋅300 forts1 match⋅256 trees1 fort⋅1 forest684 trees=3200 forests57 weeks≈\frac{1 \text{ fortnight}}{2 \text{ weeks}} \cdot \frac{1 \text{ match}}{1 \text{ fortnight}} \cdot \frac{300 \text{ forts}}{1 \text{ match}} \cdot \frac{256 \text{ trees}}{1 \text{ fort}} \cdot \frac{1 \text{ forest}}{684 \text{ trees}} = \frac{3200 \text{ forests}}{57 \text{ weeks}} \approx 56.1403509

K = 56.1403509 ⋅\cdot J

12. How many pieces of pencil lead does Alice use?

l = 10 Sudokus46 Boggles⋅58 squares1 Sudoku⋅1 number1 square⋅1 lead400 numbers=29 lead920 Boggles≈\frac{10 \text{ Sudokus}}{46 \text{ Boggles}} \cdot \frac{58 \text{ squares}}{1 \text{ Sudoku}} \cdot \frac{1 \text{ number}}{1 \text{ square}} \cdot \frac{1 \text{ lead}}{400 \text{ numbers}} = \frac{29 \text{ lead}}{920 \text{ Boggles}} \approx 0.0315217391

L = 0.0315217391 ⋅\cdot K

13. If the spectators do L waves, how many combined cups of water did all athletes drink?

m = 1 lap1 wave⋅81 leaps per athlete1 lap⋅1 cup896 leaps per athlete⋅12 athletes=243 cups224 waves≈\frac{1 \text{ lap}}{1 \text{ wave}} \cdot \frac{81 \text{ leaps per athlete}}{1 \text{ lap}} \cdot \frac{1 \text{ cup}}{896 \text{ leaps per athlete}} \cdot 12 \text{ athletes} = \frac{243 \text{ cups}}{224 \text{ waves}} \approx 1.08482143

M = 1.08482143 ⋅\cdot L

14. How many teddy bears’ worth of tickets does he win in M hours of playing pinball?

n = 1 ball1 hr⋅23000 points1 ball⋅9 tickets170 points⋅1 teddy bear1530 tickets=230 teddy bears289 hr≈\frac{1 \text{ ball}}{1 \text{ hr}} \cdot \frac{23000 \text{ points}}{1 \text{ ball}} \cdot \frac{9 \text{ tickets}}{170 \text{ points}} \cdot \frac{1 \text{ teddy bear}}{1530 \text{ tickets}} = \frac{230 \text{ teddy bears}}{289 \text{ hr}} \approx 0.795847751

N = 0.795847751 ⋅\cdot M

15. How many containers of sprinkles does she consume?

o = 10080 min1 week⋅1 episode30 min⋅83 spoons1 episode⋅5 sprinkles1 spoon⋅1 container3960 sprinkles=1162 containers33 weeks≈\frac{10080 \text{ min}}{1 \text{ week}} \cdot \frac{1 \text{ episode}}{30 \text{ min}} \cdot \frac{83 \text{ spoons}}{1 \text{ episode}} \cdot \frac{5 \text{ sprinkles}}{1 \text{ spoon}} \cdot \frac{1 \text{ container}}{3960 \text{ sprinkles}} = \frac{1162 \text{ containers}}{33 \text{ weeks}} \approx 35.2121212

O = 35.2121212 ⋅\cdot N

These equations mostly create a chain of multipliers, but problem 6, F = f ⋅\cdot (E + 1)F, adds a constraint to determine a single solution. We can express all variables in terms of E to obtain the simplified equation E = 0.973133127(E + 1). A fun way to solve for the variables is to set the products of the left-hand and right-hand sides of the system of equations equal to each other, which gives the same equation. Thus, E = 36.220558. Using this value, we can then solve for the remaining variables:

A = 365.130307 B = 243.549683 C = 3.401297 D = 61.73587 E = 36.220523
F = 0.11723 G = 642.356164 H = 1.690411 I = 10.244915 J = 9.024244
K = 506.624225 L = 15.969677 M = 17.324248 N = 13.787464 O = 485.485854


2 Elementary Math

In Part 2, we take the answers from Part 1 and plug them into the given expressions to solve. These values correspond to the atomic numbers of elements in the periodic table. Putting together the symbols of the elements gives us the answer SYNTHESIS.

Expression AnswerSymbol
1. ⌊Mln⁡(CAFFEINE)L⌋\left \lfloor \frac{M\ln{(CAFFEINE)}}{L} \right\rfloor 16 S
2. ⌈HH⌉⋅⌈K⌉\sqrt{ \lceil HH \rceil \cdot \lceil K \rceil} 39 Y
3. log⁡⌊C⌋⌊B⌋+⌊GF⌋\log_{\lfloor C \rfloor} \lfloor B \rfloor+ \lfloor G^{F} \rfloor 7 N
4. −(⌊E⌋)!⌊Mtan⁡J⌋-\frac{\left(\sqrt{\lfloor E \rfloor}\right)!}{\lfloor M \tan J \rfloor} 90 Th
5. gcd(⌈A⌉,⌈B⌉)+⌈Dsin⁡(LO)⌉gcd(\lceil A\rceil,\lceil B \rceil) + \lceil D \sin{(LO)} \rceil 99 Es
6. ⌊DGKarctan⁡J⌋\left\lfloor \frac{DG}{K \arctan J} \right\rfloor 53 I
7. ⌈(log⁡JION)H⌉\lceil (\log_{J} ION)^{H}\rceil 16 S

Authors' Notes

  • The crew thought it would be fun to include a "full" and "snapped" puzzle that would be exactly the same, and somehow, this was the puzzle that ended up being that.
  • The original idea was to just have a bunch of math problems about rates, but we wanted to make it more fun. Julz once saw a wraparound math problem set (CHMMC 2010 Mixer Round) and thought it might be interesting to write one. Famous last words D:
  • We also added a lot of minithemes so that people wouldn't associate it too much with doing homework and hopefully be entertained while doing math:
    1. Party time! This was one of the last themes we came up with after listing out existing categories and trying to pick something else for variety. Steph changed the “[person]” placeholder to Julz when she was away from the computer, and it ended up being all of our test-solvers’ favorite story... For the 0.1% of you who know Julz personally, we hope this brought you joy as well.
    2. Snoo is Reddit’s mascot, and we decided to pull him away from surfing the web to surf some waves instead!
    3. The fact that you always play one more game of Jeopardy! than you win helped us define the constraint for this puzzle.
    4. Budveirus - a digital pandemic!
    5. Lilo and stitches :)
    6. Fun fact: Steph was the only one on the Puzzle Potluck team who knew the origin of the word “fortnight”... three writers separately guessed “the amount of time people used to spend in forts”. Also we wanted to see how many times we could say fortnight in a row and still have it make sense :)
    7. Who better to Netflix and chill than Elsa?
  • At one point in our puzzle construction, we accidentally transcribed one of our coefficients as 254 instead of 265. We didn’t realize this until our test solvers got stuck and we compared spreadsheets... and then had to rewrite a decent portion of Part 1 and all of Part 2 to make the correct values work nicely together. It was a very sad time.
  • Best Wrong Answers:
    Wrong AnswerSubmitted by:
    ISTILLHAVEBOWLINGBALLPTSDPlant Parents
    IHATEDTHISCLASSGBTW
    IFAILEDCHEMFORAREASON
    FUCKMYLIFE
    		no gnus is good gnus

Stats

  • 434 solves
  • 430 incorrect guesses
  • Most common incorrect guess: SYNTHETIC (guessed 24 times)
  • First solve: Eclectic Circle of /r/PictureGame in 36 minutes and 18 seconds

PUZZLE POTLUCK 3