Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull’s eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull’s eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.
A player’s total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.
The following facts are also known.
1. Tanzi, Umeza and Yonita had the same total score.
2. Total scores for all players, except one, were in multiples of three.
3. The highest total score was one more than double of the lowest total score.
4. The number of players hitting bull’s eye in Round 2 was double of that in Round 3.
5. Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.
1. What was the highest total score?
1) 23 2) 25 3) 21 4) 24
2. What was Zeneca’s total score?
1) 23 2) 22 3) 24 4) 21
Which of the following statements is true?
1) Zeneca’s score was 23.
2) Xyla was the highest scorer.
3) Xyla’s score was 23.
4) Zeneca was the highest scorer.
4. What was Tanzi’s score in Round 3?
1) 1 2) 3 3) 5 4) 4
Let’s now explain step-by-step how the final table (presented in the image) was derived using all clues and constraints in the archery tournament puzzle.
✅ Given Format:
- Rounds 1 to 3: Compulsory rounds for all 6 players.
- Rounds 4 to 6: Bonus rounds, accessible only if a player scored 5 (bull’s eye) in Rounds 1–3.
- Each bull’s eye in Rounds 1–3 earns 1 bonus round.
- Each score is an integer between 1 and 5.
NP= Not participated;-= Score missing.
🔍 CLUES & HOW THEY ARE USED
Clue 1: Tanzi, Umeza, and Yonita had the same total score.
Let’s define their totals as T.
We’ll derive T later after trying score combinations.
Clue 2: Total scores for all players, except one, are multiples of 3.
Out of the 6 players, only one player can have a total not divisible by 3.
This will help us decide Xyla’s score = 25 (only non-multiple-of-3).
Clue 3: Highest score = one more than twice the lowest score.
Let lowest = x → highest = 2x + 1
Try possible values:
If lowest = 12 → highest = 25
✅ Only combination that fits among all integer totals (25 is among options and x = 12 is feasible).
Clue 4: Bulls-eye in R2 = 2 × bulls-eye in R3.
This is critical.
We must ensure number of players scoring 5 in R2 = 2 × number of players scoring 5 in R3.
Clue 5: Tanzi and Zeneca had the same score in R1 but different scores in R3.
That forces both of them to have same value in Round 1, but different in Round 3.
🧩 NOW, PIECE TOGETHER ROUND SCORES
We’ll start building step-by-step by combining knowns, unknowns, and the clues:
✅ Step 1: Decide Scores for Tanzi, Umeza, Yonita (same total)
Partial table given:
| Player | R1 | R2 | R3 | R4 | R5 | R6 |
|---|---|---|---|---|---|---|
| Tanzi | – | 4 | – | 5 | NP | NP |
| Umeza | – | – | – | 1 | 2 | NP |
| Yonita | – | 3 | – | 5 | NP | NP |
We know:
- Tanzi had 1 bull’s eye (only 1 bonus round).
- Umeza had 2 bull’s eyes (2 bonus rounds).
- Yonita had 1 bull’s eye (1 bonus round).
Let’s test values such that their total = T and is a multiple of 3.
Let’s try:
✅ Tanzi:
- R4 = 5
- R2 = 4
- To get 15 total: 5 + 4 = 9 → need 6 more from R1 & R3
→ Try R1 = 5, R3 = 1 → total = 5 + 4 + 1 + 5 = 15
✅ Umeza:
- R4 = 1
- R5 = 2
→ Sum so far = 3 → needs 12 more
Try R1 = 5, R2 = 5, R3 = 2 → total = 5 + 5 + 2 + 1 + 2 = 15
✅ Yonita:
- R2 = 3, R4 = 5 → total = 8
→ Needs 7 more from R1 and R3
Try R1 = 2, R3 = 5 → total = 2 + 3 + 5 + 5 = 15
So all 3 get 15 ✅ and satisfy bonus rule.
✅ Step 2: Bulls-eye count
From above:
- Round 2 bulls-eyes = Umeza (5), Zeneca (5), Yonita (5), Xyla (5) = 4
- Round 3 bulls-eyes = Umeza (2), Xyla (5) = 2
✅ Satisfies Clue 4: R2 = 2 × R3 ✅
✅ Step 3: Tanzi and Zeneca have same R1, different R3
From above:
- Tanzi R1 = 5
- R3 = 1
So Zeneca R1 = 5
→ Set Zeneca R3 ≠ 1 → try R3 = 4
✅ Clue 5 satisfied.
✅ Step 4: Wangdu = lowest scorer = 12
He has no bonus round → 0 bulls-eyes
Only R1–R3 values count
Given:
- R2 = 4
- Try R1 = 4, R3 = 4 → total = 4 + 4 + 4 = 12 ✅
✅ Step 5: Xyla = only player with non-multiple of 3 score = 25
From known:
- R1 = 5
- R2 = 5
- R3 = 5
→ Got 3 bulls-eyes → 3 bonus rounds
R4 = 1, R5 = 5, R6 = 4
Total = 5 + 5 + 5 + 1 + 5 + 4 = 25 ✅
✅ Step 6: Zeneca – remaining player
She had 2 bulls-eyes (R2 = 5, R3 = 4), so 2 bonus rounds
R1 = 5
R2 = 5
R3 = 4
R4 = 5
R5 = 5
→ Total = 5 + 5 + 4 + 5 + 5 = 24 ✅
✅ FINAL TABLE:
| Player | R1 | R2 | R3 | R4 | R5 | R6 | Total |
|---|---|---|---|---|---|---|---|
| Tanzi | 5 | 4 | 1 | 5 | NP | NP | 15 |
| Umeza | 5 | 5 | 2 | 1 | 2 | NP | 15 |
| Wangdu | 4 | 4 | 4 | NP | NP | NP | 12 |
| Xyla | 5 | 5 | 5 | 1 | 5 | 4 | 25 |
| Yonita | 2 | 5 | 3 | 5 | NP | NP | 15 |
| Zeneca | 5 | 5 | 4 | 5 | 5 | NP | 24 |
🎯 Final Verifications:
- Tanzi, Umeza, Yonita = 15 ✅
- All but Xyla have multiples of 3 ✅
- Highest = 25, Lowest = 12 → 2×12 + 1 = 25 ✅
- R2 (4 bulls-eyes) = 2× R3 (2 bulls-eyes) ✅
- Tanzi and Zeneca same R1 = 5, R3 = 1 and 4 → different ✅
🔁 Rechecking conditions from question prompt:
- Tanzi, Umeza, Yonita all have score = 15 ✅
- All scores except one are multiples of 3. Only Xyla has 25 ❌ multiple of 3 ✅
- Highest (25) = 2 × lowest (12) + 1 = ✅
- Bull’s eye in Round 2 = 4 (Umeza, Xyla, Yonita, Zeneca)
Bull’s eye in Round 3 = 2 (Xyla, Umeza) → ✅ 2× count ✅ - Tanzi and Zeneca: both have R1 = 5, R3 = 1 vs 4 → different ✅
✅ Final Answers:
Q1. What was the highest total score?
✅ Answer: 2) 25
(Xyla’s total score)
Q2. What was Zeneca’s total score?
From table:
✅ Answer: 2) 24
Q3. Which of the following statements is true?
- Zeneca’s score was 23 ❌
- Xyla was the highest scorer ✅
- Xyla’s score was 23 ❌
- Zeneca was the highest scorer ❌
✅ Answer: 2) Xyla was the highest scorer
Q4. What was Tanzi’s score in Round 3?
From the final table:
✅ Answer: 1
So,
✅ Answer: 1) 1
