These are the Official Answers
for the 2021 Independence Day Fireworks.

We posted them here on August 11.

In addition, earlier in the week we mailed the answers to all competitors.

The answers and explanations below are identical to those sent in the mail, which also include
the procedure for filing a protest (i.e., an objection, which will be due by August 20) regarding any answer.

Following scoring, we'll post here any protest results and we'll print and mail everybody a complete set of results.

August 22 update:

Q4: We scored a correct as well as b: the gray other road going east from Rosthern reaches a junction on the east bank of the S. Saskatchewan River where itís possible that rule d (as close to straight as possible) actually sends us north through Batoche, then east upon Sask. 225, leading to our ending #7 south on Sask. 2 through Cudworth.

******** Final results are at the printer and will be mailed in about 10 days. ********


Note: Your BACKGAMMON play affected your Q14, Q18, and Q27 answers. Details follow with those answers.
In each case, we will score those three answers correct for you if they correspond to any of the possible correct combinations of those answers. In the final results, weíll provide a tally of everybodyís answers.

Q Answer Leg 1


b) Beaufort Sea

Yellowknife (D-5) is the closest to Qausuittuq [3 3/4 map inches] and is within sight [1/4 map inch] of incorporated BehchokÚl, so we paddle into Mountain Time Zone and through Beaufort Sea to Mackenzie Bay, thence up the Mackenzie River to Great Slave Lake and Yellowknife.[Iqaluit is not within sight of an incorporated town, and is a bit farther from Qausuittuq anyway.]


a) yes

Paddling up the Churchill River and through various lakes, we see [within 1/4 map inch] Manitoba 280 and Manitoba 391, both secondary [rectangular symbol].


d) 4

We travel upon Sask. 165 [which runs upon our principal highway for 12 miles or so in linking its oval symbols: Numbered Highway def. and note after Q3], Sask. 2, and Sask. 3 [which crosses S. Saskatchewan River with Sask. 2 in connecting its Sask. 3 symbols west near Mildred and southeast near Kinistino], then [since #5 did not place us on Sask. 2, we do not have a rule-b obligation to stay on Sask. 2] course-following rule c sends us southwest after Prince Albert to stay upon our orange multilane highway with Sask. 11 through Macdowall to #6 east at Sask. 312 near Rosthern.


b) Resource

Eastbound from Rosthern, we go through Wakaw and odd Sask. 41ís symbol to end #7 at Melfort south on Sask. 6 through Resource.


b) no

Since #9 is at T-C 16, not on T-C 16, rule b is not activated to keep us on T-C 16; rather, at Sask. 11 on the Saskatoon map, course-following rule d keeps us going ahead south off the map, where we find that weíre upon Sask. 11ís orange road down to #10 west on Sask. 15 near Kenaston.

Q Answer Leg 2


b) White Bear

#1 ends west on Sask. 44 through Cutbank [linking 44ís symbols both east toward Davidson and west near Dinsmore], then rule b keeps us on 44 through Dinsmore, then through a 44 symbol, then rule b keeps us on 44 south and west through Wartime [44 continues through its symbol near the Alberta boundary] to #2 south onto Sask. 342 through Tyner and then White Bear.


c) 2

#5 did not use the word on to place us on Sask. 19, so rule b is not active; instead, rules c and d keep us going upon 19ís road anyway as far as Chaplin, where 19 leaves us as rule d sends us ahead down Sask. 58 to #6 west on Sask. 363 through Shamrock and unincorporated Kelstern, then rule b keeps us on Sask. 363 up through unincorporated Neidpath to #7 south on Sask. 4.


b) no

At Sask. 43ís end, rule d sends us ahead up Sask. 2 through Mossbank and we reach Moose Jaw, which Sask. 39 does not reach, so we continue with rules c and d northward through Tuxford and onto Sask. 11 to the Saskatoon map, where rule d sends us ahead north onto T-C 16, then counterclockwise with Circle Dr., then ahead east off the Saskatoon map upon eastbound T-16, then after Jansen rule d sends us southward through Dafoe toward Raymore and through Regina finally to end #8 northwest on Sask. 39 at Corinne toward Rouleau.


b) no

We see river named Moose Jaw, but #10 put us on Sask. 6, which rule b keeps us on southward to end #10 west on Sask. 13 near Pangman, missing seeing Yellow Grass.


d) 3

On 223 after #14, we reach U.S. 2 at Chester, but we havenít gone through [enter, then leave] Liberty Co. yet, so we continue northward onto unpaved road, which heads eastward across 224 [taking us out of Liberty Co.], 255, and 449, then our road heads southward to #15 west on U.S. 2 through Gildford and we see Inverness, Devon, and Dunkirk on the way to Cut Bank.

Q Answer Leg 3


b) 1

Leaving Cut Bank, rule b still is keeping us on U.S. 2 (no new Action [left, right, etc.] supplanted rule b for U.S. 2), so at Browning we stay on U.S. 2 southwest to the Waterton-Glacier map (B.R. 3/a) to #2 north on Mont. 49 at East Glacier Pk. Vil., then north on U.S. 89 at Kiowa, then #3 is right onto 501 before Cardston, then, since at the Waterton-Glacier map edge weíre in Alberta, B.R. 3/b takes us to the Alberta map on page 119, where we see Del Bonita (L-17) ahead before #4 south on Alta. 62, then B.R. 3/b takes us back to the Montana map, where 213ís road takes us through Santa Rita to rule d southeast at Cut Bank to #5 south on I-15 near Shelby.


c) 2

#5 ends by placing us on Mont. 200, on which with B.R. 3/a we go to the Missoula map on p. 61 (seeing East Missoula there), then back on the state map rule b sends us north at interchange 96 to stay on 200 and see Old Agency before #6 left after Perma.


c) 3

On the Missoula map, #8 is south on U.S. 93 (identified both northwest and south; BR 90ís shield doesnít affect U.S. 93), then rule b keeps us on U.S. 93 through that BR 90 shield, a U.S. 93 shield, and a U.S. 12/93 shield.


This answer depends on your Backgammon play with Teton Tess: your answer should be:



b) Wise River

if you threw an odd number and therefore went left at Wisdom; in this case, you see the town Wise River on the way to #12 at interchange 102;


or a) Polaris

if you threw an even number and therefore went right at Wisdom; in this case, you see the town Polaris on the way to #12 at interchange 59.


a) yes

#13 does not use the magic word on to place us on U.S. 12, so on the Helena map rule c sends us up Last Chance Gulch upon orange multilane to #14 south at Cedar St.

Q Answer Leg 4


a) yes

We reach Four Corners upon orange multilane highway (after Mont. 85 symbol), so in Leg 4 we continue by using rule c to go east, staying upon our orange multilane highway, then for #2 we go through junction with gray other road, then rule d sends us ahead onto eastbound I-90 to #2 south onto U.S. 89 at interchange 333, then on the Yellowstone map on p. 116 #3 is south on U.S. 89 at Mammoth, then rule b keeps us on U.S. 89, seeing town Old Faithful on the way to #4 left through West Thumb.


b) Buffalo Bill S.P.

After Tower Jct., U.S. 212 takes us back up to Montana but then back down to Wyoming, so at the mapís edge B.R. 3/b takes us to the Wyoming map on p. 116, on which U.S. 212 takes us up to #5 at Red Lodge, then right on Mont. 72 (which does not show the town Belfry that is shown on p. 61: yes, its schoolís sports teams are the Bats), then before #6 on Alt 14 at Cody we see nearby Buffalo Bill S.P.


This answer depends on your Backgammon play with Bighorn Bess: your answer should be:



a) Banner

if you threw an odd number and therefore went left on Interstate 90 at interchange 58; in this case, #9 is left onto gray other road just past Banner, then #10 (rule a, overriding rule d) is north on U.S. 87, then #11 is right on U.S. 14 near Sheridan, then you see Banner first from U.S. 14;


or c) Spotted Horse

if you threw an even number and therefore went right on Interstate 90 at interchange 58; in this case, #9 is left onto gray other road at interchange 65, then #10 (rule a, overriding rule d) is north on Wyo. 341 at Arvada, then #11 is right on U.S. 16, then you see Spotted Horse first.


a) yes

After #12 left onto unpaved road at the first junction in Converse Co., back in Campbell Co. the unpaved road ends and we continue onto solid gray other road, which rule c keeps us upon west to Wyo. 59, so #13 puts us on northbound Wyo. 59 past Wright and up to Gillette to end #13 right on U.S. 16, then immediately we see Sleepy Hollow.


c) 3

B.R. 3/a takes us to the Black Hills Region map on p. 93 for #14 right on U.S. 85, then we go through one U.S. 85 highway shield on that map, then back on the Wyo. map we cross county boundary into Niobrara Co. and go through another U.S. 85 shield, then #15 is west on U.S. 18 at Lusk through a U.S. 18/20 shield.

Q Answer Leg 5


b) no

Weíre still on U.S. 87 as we leave Glenrock, so rule b keeps us on U.S 87 on the Casper map to #2 left at interchange 189, then #3 is south onto Wyo. 254 at the next interchange.


a) yes

BR 20 ends soon after we turn on it to end #3, then we go back to the Wyo. map to rule d southwest at Shoshoni (weíre not on regular U.S. 20) and through Riverton to rule d ahead at county seat Lander onto Wyo. 131 to #4 left on Wyo. 28, then immediately we see town Atlantic City.


a) yes

#6 is right on Wyo. 789 at town Muddy Gap, then rule b keeps us on 789 to see Muddy Cr. before #7 at Baggs.


b) 1

#8ís highway symbols are a 230 after Riverside and another 230 after Woods Landing [we donít go through 10ís symbol], then another 230 on the Laramie map Ė only 3 so far, so we continue with rules c and d onto eastbound Snowy Range Rd., then Harney St., northward onto Inca Dr., westward onto Reynolds St., then onto Curtis St. through a BR 80 symbol to southward onto Pierce St. finally to #8 east onto Snowy Range Rd., continuing as above to #9 south on U.S. 287 at 3rd St., then back on the Wyo. map we see town Tie Siding [named as a marshalling point for hewn railroad ties] before leaving Wyo.


b) Promenade Shops

Southbound upon orange multilane highway on the Fort Collins map (we were not placed on U.S. 287), in Loveland we reach a situation like Leg 2ís note about one way routes in Billings: here we must avoid Lincoln Av.ís northbound one way route by diverting to take the southbound one way route upon Cleveland Av. to #11ís first opp., at U.S. 34, then after 1st St. the road ahead is orange multilane again, so rule c sends us acutely left to stay upon our red principal highway up Lincoln Av. across 1st St. again to #11ís second opp., at U.S. 34 again, where we go east on U.S. 34, then we see Promenade Shops ahead before #12 at I-25ís interchange 257.

Q Answer Leg 6


c) go through S. Greeley

Eastbound from Severance, rule d sends us ahead at Colo. 392 onto unpaved road, which zigzags up to Colo. 14, where rule d sends us northwest onto 14, then #2 is north at interchange 269 back on the Fort Collins map, then up on the Cheyenne map on p. 116 (B.R. 3/a) #2 ends at interchange 12 southeast on U.S. 85, which takes us through S. Greeley, Wyoming, on the Cheyenne map before returning us to Colorado.


This answer depends on your Backgammon play with Kiowa Wes: your answer should be:



b) 1

if you threw an odd number and therefore went left on U.S. 36 at Last Chance; in this case, rule b keeps you on U.S. 36 all the way to eastern Kansas on p. 41 for #5 north onto U.S. 75ís road past Sabetha, then on the Nebraska map on p. 63 #6 is west on U.S. 136 at Auburn, then #7 is south on U.S. 77 at Beatrice, then #8 is near Marysville right back on westbound U.S. 36, which rule b keeps you on to #9 east on I-70 at interchange 316 in Arapahoe Co., which you see;


or a) 0

if you threw an even number and therefore went right on U.S. 36 at Last Chance; in this case, #5 is east onto I-70 at interchange 316, then #6 is west on U.S. 24 at interchange 438 when you see Burlington, then #7 is south on U.S. 385 at Burlington, then #8 is west on U.S. 40 at Cheyenne Wells, then #9 is east on I-70 at interchange 363.


d) 4

After #11 south onto unpaved road at Wild Horse, we enter Kiowa Co., in which we cross Colo. 96 and our road heads east, then north to Eads, where we havenít left Kiowa Co. yet [Go Through def.], so rule d keeps us going north through Eads and out of Kiowa Co. to U.S. 40 near Kit Carson, where rule d sends us east through Cheyenne Wells to the Kansas map, where at Oakley rule c sends us south to stay upon red principal highway with U.S. 83 to finally go west on Kansas 96 at Scott City, then we see Wichita County (its seat is Leoti) and after U.S. 385 go back to the Colo. map, where we see Kiowa County and at Eads (#12 placed us on Kansas 96, not Colo. 96, which rule b canít keep us on) rule c sends us north to stay upon principal highway to rule d east upon U.S. 40 again as we see town Kit Carson as well as Cheyenne County, then #13 is south on U.S. 385 just after Cheyenne Wells.


c) Lamar

#14 is west at Sheridan Lake [rule a overrides rule b, in the process canceling rule b for U.S. 385], then immediately south at U.S. 385, then at Granada we are at a town (and now we are not on U.S. 385), so rule d keeps us going ahead south onto unpaved road, which then heads west, then north to #15 west on U.S. 50 toward Lamar, which soon we see.


c) no; neither see nor go through

#17ís end at Hasty does not place us on U.S. 50, so at Las Animas rule d sends us ahead south down Colo. 101 to #18 south on U.S. 160 just above Pritchett, then we cross county boundary to #19 east at our red principal highway at Kim onto unpaved road that takes us to #20 at the junction above Campo.


d) no

There are 19 possible sets of tosses (each set made up of 1 odd toss and 2 even tosses, with the sum of the 3 tosses being greater than 5 and less than 12, and with no move ending on the lower boardís point 2 or on the upper boardís point 6 [each is blocked by multiple white checkers]).



For example, one possible set is 2 + 1 + 4 = 7, ending on the upper boardís point 2; another possible set is 3 + 4 + 2 = 9, ending on the upper boardís point 4.



Since the sum of 1 odd + 2 even itself has to be odd, that rules out 6, 8, and 10.And 11 is ruled out because any of its sets of moves would end up on the upper boardís blocked point 6.



So each of the possible sets of tosses must total either 7 or 9, inevitably ending up on the upper boardís point 2 or point 4.



Here are the 19 possible sets of tosses, each summing to either 7 or 9: 6+2+1; 6+1+2; 5+2+2; 3+4+2; 3+2+4; 3+2+2; 2+6+1; 2+5+2; 2+4+3; 2+4+1; 2+3+4; 2+3+2; 2+1+6; 2+1+4; 1+6+2; 1+4+4; 1+4+2; 1+2+6; 1+2+4.

Q Answer Leg 7


a) yes

We end Leg 6 south on U.S. 287 to Cactus, then [thereís no Action at Cactus to supplant rule b] we continue still on U.S. 287, so, after we see Wonderland Amusement Park and Zoo on the Amarillo map, rule b keeps us on 287 east at interchange 70, then #2 is north at interchange 75, then rule b keeps us going counterclockwise on 335 a full circuit across U.S. 287 [with St. Francis Av.] finally to #3 east on I-40 back at interchange 75.


c) West Point

We donít count I-40ís two blue symbols (Map Legend: theyíre rest areas, not waysides); we do see the three waysides just past Goodnight, then another wayside before Clarendon, but we need one more so we continue on 287 and see fifth wayside near Hedley, then continue on 287 to #6 southwest on U.S. 70 near Vernon, then we go through U.S. 70 symbols in Foard Co., Motley Co., Floyd Co., Lamb Co., and in N.M. after Clovis, then on the N.M. map #7 is east on U.S. 380 through Roswell, then back in Texas we go through West Point in Lynn Co. first.


c) West

After #8 south at U.S. 77, rules c and d take us to #9 at interchange 19 east on Northeast Loop, which ends at Airport Frwy. (the Loop to the south is East Loop, not Northeast), so rules c and d keep us going upon Airport Frwy., then Texas 183, I-35 E, Corinth St., Lancaster Rd., Texas 342, Dallas Av., and back on the state map onto I-35E just after Red Oak to end #9 south at I-35W above Hillsboro, then we see town West first.


a) Central

#11 is southeast not on U.S. 287 when we see Texas St. R.R. Hist. Pk. but on U.S. 69 when we see Texas State Railroad, then we see town Central.


b) 2

#13 is south on U.S. 287 soon after we arrive on the Beaumont map [rule a overrides rule c; and, although due north is not straight toward the top of this map, the compass directions fit within the Action def.ís 45į leeway anyway], then, since all I-10/U.S. 287 interchanges are numbered, rule b keeps us on 287 southeast at interchange 849 to #14 southwest on Texas 73 [7+3=10] after Babe D. Zaharias Mem., then rule d takes us to the map edge where, back on the state map, we find that weíre back on Texas 73, which takes us to interchange 828, where rule d is ahead onto westbound I-10 to the Houston map, where we go through interchange 788.

Q Answer Leg 8


b) 1

Leg 7ís #15 placed us on I-69 [not U.S. 59], so back on the state map we travel upon U.S. 59ís roads seeing Louise, Edna, and Inez, then near Victoria rule c keeps us upon orange multilane southwest with U.S. 77 to #2 north on Alt 77 near Refugio in Refugio Co., then we see town Blanconia, then Alt 77 ends near Hallettsville, so rules c and d send us east through Sublime upon Alt 90 back to the Houston map, where eventually we go ahead onto Wayside Dr.ís red principal highway across I-45, then at the junction after Navigation Blvd. (weíre not using rule b to stay on Alt 90) rule c doubles us back to stay upon our red principal highway southbound back across Navigation Blvd., then rule d sends us back onto southwestbound Wayside Dr. and across I-45 to immediately use topmost rule a [overriding rule c] for #3 west on Alt 90 [numberís first digit is 9], then back on the state map rule b keeps us on Alt 90 westbound through Hallettsville, Shiner, and Seguin to #3 west on I-10.


c) 4

We do not travel upon any section of U.S. 287 in Montana: in Leg 3ís #5 we only pass the northern end of U.S. 287 as we go through Choteau on U.S. 89; on Mont. 200 after #5 we only cross 287 near Milford Colony; in #16 we only cross 287 when eastbound on I-90 near Three Forks; Leg 4ís #2 is south onto U.S. 89 from I-90ís interchange 333, then #3 is on U.S. 89 at Mammoth in Wyoming, ceasing our chance to travel upon U.S. 287 in Montana.



These are the first sections of U.S. 287 for each of the other 4 states:



Wyoming: in Leg 4 weíre upon U.S. 287 in Yellowstone as we go through town Old Faithful between #3 & #4



Colorado: in Leg 5 weíre upon U.S. 287 as we enter Colorado for #10



Oklahoma: in Leg 6 weíre upon U.S. 287 as well as U.S. 385 as we enter Oklahoma after #20



Texas: in Leg 6 we turn on U.S. 287 toward Cactus in ending #21


d) 3

After #4, we head down U.S. 385 (not a state highway), then loop back up Texas 118 through its first symbol, also seeing Terlingua Cr., then we continue through Alpine (at Coyanosa Draw seeing county Presidio nearby to the west) to go through a second Texas 118 symbol, then we see Casket Mtn. ahead before #5 southwest on Texas 17 at Fort Davis.


d) 3

We see Fort Leaton St. Hist. Site on p. 99 before #6 sends us to p. 128, where rules c and d take us across Continental Divide at La Junta, then down toward Esperanza, but at the next junction our road curves back northbound through Tůnichi to end #6 south on Mexico 15 after La Colorada.


b) Acapulco

#7 is south onto 37 after Zamora, then left on 200 through La Uniůn to see Acapulco first.


c) 2

The wide red principal highway upon which we enter Guatemala ends at Quezaltenango, from which we continue upon a narrow red other through highway, which rule c keeps us upon as twice we cross the wide red principal highway that comes down from Mexico 190, then rule d puts us onto that road as it goes to the capital Guatemala.