Puzzle 50: The Champions Trial

Puzzle Walkthrough

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Blue equals Patient (Clue 11), use Clue 2’s first part: the 8:05 Sandbag belongs to Intuitive or Patient. That means the 8:05 Sandbag belongs either to Blue or to Intuitive.

From Clue 10, Redemption has the fastest Sandbag. The four Sandbag times are 7:18, 8:05, 9:33, and 10:42, and the fastest is 7:18. Therefore Redemption’s Sandbag is 7:18.

From Clue 6, Jane’s Sandbag is neither 7:18 nor 10:42. So Jane is not Redemption and Jane does not have 10:42.

From Clue 13, the 10:42 Sandbag owns the fastest Final Flame time overall. This means whoever has 10:42 has the very best Final Flame time.

Now consider Clue 12’s structure. Analytical’s Final Flame is slower than Intuitive’s and exactly forty-nine seconds slower than Blue’s. Therefore Blue has a faster Final Flame than Analytical, and Intuitive also has a faster Final Flame than Analytical. Pair this with Clue 13: the single fastest Final Flame belongs to the 10:42 runner. Thus the 10:42 runner’s Final Flame must be faster than Blue’s Final Flame as well. Therefore the 10:42 runner is not Analytical and is also not Blue, because Blue’s Final Flame cannot be the fastest overall if Analytical is set relative to Blue. So 10:42 belongs to someone who is neither Blue nor Analytical.

Return to Clue 9. Harper is Blue or Red. If Harper were Blue, then Harper would be Patient (Clue 11). Keep both possibilities open for now.

Use Clue 3’s Memory ordering: Finn faster than Mina, Mina faster than Harper. Use Clue 9’s add-on that Blue is faster than Finn on Memory. So Memory order from fastest toward slower must place Blue ahead of Finn, Finn ahead of Mina, and Mina ahead of Harper. That fixes the full Memory ranking: Blue first, then Finn, then Mina, then Harper.

Now apply Clue 1 and Clue 5 about Victory’s Memory being slower than Blue’s and slower than Finn’s. In the ranking we just established, only Mina and Harper are slower than Finn. But Clue 3 already says Mina is faster than Harper. Victory must be somewhere after Finn; coupled with Clue 1 and the full ranking, the only spot compatible is Mina or Harper. However Clue 3 requires Mina to be faster than Harper, and we already know Victory is slower than Finn and slower than Blue; it will be consistent shortly once we pin individual identities.

Bring in Clue 7: Green is neither Glory nor Redemption, so Green is Family or Victory.

Consider the fastest Sandbag from Clue 10: Redemption has 7:18. From Clue 9, Harper’s Sandbag is faster than Glory’s Sandbag. The fastest Sandbag is Redemption at 7:18. If Harper were Redemption at 7:18, then Harper would necessarily be faster than Glory, which aligns, but we still must satisfy the Memory ordering and headband rules.

Now use Clue 2’s second part: Analytical did not post the fastest Sandbag time, so Analytical is not Redemption. So Analytical is not at 7:18.

Leverage Clue 4: Red headband’s Sandbag is at least forty seconds faster than Family’s Sandbag. The possible gaps between Sandbag times must allow a difference of at least forty seconds. Compare each pair to ensure a viable pairing later; keep this in mind.

Use Clue 6 again: Jane is not Aggressive, and Jane’s Sandbag is neither 7:18 nor 10:42. So Jane’s Sandbag is either 8:05 or 9:33. From Clue 2, 8:05 belongs to Intuitive or Patient. If Jane had 8:05, then Jane would be Intuitive or Patient. But from Clue 11, Patient is Blue. That would force Jane to be Blue if she were Patient. Keep this as a branch to check against other constraints.

Use Clue 8: Intuitive’s Memory is slower than Blue’s but faster than the 9:33 runner’s Memory. Since Blue is the fastest Memory overall, Intuitive must be second-fastest Memory, which is Finn in the ranking we established. Therefore Intuitive must be Finn. That also fixes the 9:33 runner’s Memory as slower than Finn’s Memory. From the ranking, slower than Finn’s could be Mina or Harper, which is fine.

From the deduction above, Finn is Intuitive. Return to Clue 2’s first part: the 8:05 Sandbag belongs to Intuitive or Patient. Since Finn is Intuitive, either Finn has 8:05 or the Blue headband has 8:05. Keep both options for a moment.

Use Clue 12 with our new knowledge. Analytical’s Final Flame is forty-nine seconds slower than Blue’s, and Analytical is slower than Intuitive on Final Flame. Since Intuitive is Finn, Finn’s Final Flame is faster than Analytical’s. Also, Blue’s Final Flame is the fastest among these two by forty-nine seconds. Clue 13 says the 10:42 runner has the single fastest Final Flame of everyone, faster even than Blue’s. Therefore the 10:42 runner is neither Finn nor Blue nor Analytical.

Now apply Clue 9’s first sentence: Harper wore Blue or Red. We will test which option fits all constraints.

Test Harper as Red. If Harper is Red, then by Clue 4 Red’s Sandbag is at least forty seconds faster than Family’s Sandbag. Also, Redemption is the fastest Sandbag at 7:18 (Clue 10). From Clue 9’s second sentence, Harper’s Sandbag is faster than Glory’s. That fits if Harper’s Sandbag is very quick. This path remains open.

Test Harper as Blue. If Harper is Blue, then Harper is Patient (Clue 11). Then Finn is Intuitive (as shown). Clue 8 demands Intuitive’s Memory slower than Blue’s; that is consistent with our ranking since Blue is the fastest Memory overall and Finn is second. However, Clue 6 says Jane is not Aggressive. With Harper set to Blue equal Patient, the remaining approaches for Jane would be Analytical or Intuitive or Aggressive, but Intuitive is already Finn, and Aggressive is forbidden for Jane. That would force Jane to be Analytical. Keep that in mind and test it against other constraints.

Now use the remaining approach pool and Clue 2’s second part: Analytical did not post the fastest Sandbag. The fastest Sandbag is Redemption at 7:18. So Analytical is not Redemption. Clue 10 already stated that.

Turn to Clue 13 again. The 10:42 Sandbag has the fastest Final Flame overall. Check Clue 6: Jane’s Sandbag is not 10:42, so Jane is not the overall fastest Final Flame owner.

Bring in the Memory ranking we locked: Blue, then Finn, then Mina, then Harper. From Clue 3, Mina is faster than Harper and slower than Finn, which matches perfectly.

Now resolve motivations using the headband and color constraints. From Clue 7, Green is not Glory and not Redemption. From Clue 10, Redemption owns the fastest Sandbag at 7:18, and from Clue 4, Red’s Sandbag is at least forty seconds faster than Family’s. A clean fit emerges if Redemption takes 7:18 on someone who is neither Green nor Analytical, and Red is a separate person whose Sandbag is also quick relative to Family.

Check a concrete fit that satisfies all interlocking constraints:

  1. Let Harper be Red with the fastest Sandbag at 7:18, making Harper Redemption. This satisfies Clue 10 and puts Harper’s Sandbag faster than Glory’s (Clue 9). It also respects Clue 2’s second part since Analytical is not the fastest Sandbag.
  2. Since Harper is Red, Mina cannot be Red or Green (Clue 3), so Mina must be Yellow or Blue. But Blue is tied to Patient (Clue 11), and Blue’s Memory must be fastest overall. Mina’s Memory is not the fastest; it is third in the ranking. Therefore Mina cannot be Blue and must be Yellow.
  3. With Harper set to Red and Mina set to Yellow, the remaining colors for Finn and Jane are Blue and Green. Blue must be Patient (Clue 11). Finn is Intuitive (from Clue 8 deductions), so Finn cannot be Blue. Therefore Jane is Blue and Patient; Finn is Green and Intuitive. This also satisfies Clue 7 because Green is not Glory or Redemption; Finn as Green can be Family or Victory.
  4. Use Clue 5 and Clue 1 together regarding Victory’s Memory being slower than both Finn and Blue. Since Finn and Blue occupy the top two Memory spots, Victory must be either Mina or Harper. But Clue 10 already set Harper to Redemption, so Victory must be Mina. Thus Mina is Victory.
  5. With Mina as Victory and Harper as Redemption, the remaining motivations for Finn and Jane are Family and Glory. Bring back Clue 4: Red headband’s Sandbag is at least forty seconds faster than Family’s Sandbag. Harper is Red at 7:18, so Family’s Sandbag must be 8:05 or slower and at least forty seconds slower than 7:18. The only Sandbag times at least forty seconds slower than 7:18 are 8:05, 9:33, and 10:42. Check Clue 13: 10:42 has the fastest Final Flame and is neither Blue nor Analytical. Since Jane is Blue, Jane cannot have 10:42, and Clue 6 already forbade 10:42 for Jane. That leaves 10:42 to Finn or Mina or Harper, but Harper already has 7:18. Mina’s Sandbag cannot be 10:42 if it must also make the Memory relations from Clue 8 work with the 9:33 condition. The consistent placement is Finn at 10:42.
  6. Assign Finn the 10:42 Sandbag. From Clue 13, Finn then owns the fastest Final Flame overall. From Clue 2’s first part, the 8:05 Sandbag belongs to Intuitive or Patient. Finn is Intuitive, so Finn could have 8:05, but we have just placed Finn at 10:42 to satisfy the Final Flame condition. Therefore the 8:05 Sandbag must belong to Patient. Patient is Blue, which is Jane. So Jane has 8:05.
  7. With Sandbags now at Harper 7:18, Jane 8:05, Finn 10:42, Mina must be 9:33 by elimination. This matches Clue 8’s requirement that Intuitive’s Memory (Finn) is faster than the 9:33 runner’s Memory (Mina), while still being slower than Blue’s Memory.
  8. Clue 6 also required Jane not to be Aggressive, and we already have Jane as Patient, consistent.
  9. Set the remaining motivations. We have Harper as Redemption and Mina as Victory. From Clue 9, Harper’s Sandbag is faster than Glory’s; that is true because Harper is the fastest at 7:18. The remaining motivations are Family and Glory for Finn and Jane. Clue 4 requires Red to be at least forty seconds faster than Family; Harper at 7:18 is at least forty seconds faster than 8:05, 9:33, and 10:42, so Family can be any of the others. But we also need Clue 7 satisfied: Green is neither Glory nor Redemption. Finn is Green, so Finn cannot be Glory and cannot be Redemption. Therefore Finn must be Family. That forces Jane to be Glory.
  10. Approaches. We have Jane as Patient and Finn as Intuitive. Clue 6 forbids Jane from Aggressive, already met. Clue 2 forbids Analytical from having the fastest Sandbag; Harper has the fastest Sandbag and therefore Harper cannot be Analytical. With Jane as Patient and Finn as Intuitive, the remaining approaches for Harper and Mina are Analytical and Aggressive. Clue 12 says Analytical’s Final Flame is forty-nine seconds slower than Blue’s Final Flame and also slower than Intuitive’s Final Flame. Place Analytical on Mina and Aggressive on Harper. This avoids making the fastest Sandbag runner Analytical and obeys the Final Flame comparison.
  11. Final Flame times. From Clue 13, Finn at 10:42 has the fastest Final Flame overall, so Finn must take 11:36. Clue 12 requires Analytical to be forty-nine seconds slower than Blue’s Final Flame and slower than Intuitive’s. Jane is Blue; give Jane 12:58, then Analytical must be 13:47, which fits forty-nine seconds slower than 12:58. That places Mina at 13:47. The remaining Final Flame time, 15:01, goes to Harper. This also keeps Analytical’s Final Flame (Mina at 13:47) slower than Intuitive’s Final Flame (Finn at 11:36), matching Clue 12.

All clues are satisfied with a single consistent assignment.

Answers

Finn
Memory Challenge: 12:07
Sandbag Run: 10:42
Final Flame: 11:36
Motivation: Family
Mental Approach: Intuitive
Headband Color: Green

Jane
Memory Challenge: 10:52
Sandbag Run: 8:05
Final Flame: 12:58
Motivation: Glory
Mental Approach: Patient
Headband Color: Blue

Harper
Memory Challenge: 14:43
Sandbag Run: 7:18
Final Flame: 15:01
Motivation: Redemption
Mental Approach: Aggressive
Headband Color: Red

Mina
Memory Challenge: 13:31
Sandbag Run: 9:33
Final Flame: 13:47
Motivation: Victory
Mental Approach: Analytical
Headband Color: Yellow

 

Here are the total times for each finalist in The Champions Trial based on their three challenge times:

Finn
Memory Challenge: 12:07
Sandbag Run: 10:42
Final Flame: 11:36
Total Time: 34:25

Jane
Memory Challenge: 10:52
Sandbag Run: 8:05
Final Flame: 12:58
Total Time: 31:55

Harper
Memory Challenge: 14:43
Sandbag Run: 7:18
Final Flame: 15:01
Total Time: 37:02

Mina
Memory Challenge: 13:31
Sandbag Run: 9:33
Final Flame: 13:47
Total Time: 36:51

Champion:
Jane has the lowest total time of 31:55 and is crowned the Survivle Season 1 Champion.

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