Problem 19 · 2009 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcasework
Andrea, Branimir, Celestin and Doris (not necessarily in this order) finish a fencing tournament ranked first to fourth. Adding Andrea’s, Branimir’s and Doris’s ranks gives a total of 6. Adding Branimir’s and Celestin’s ranks gives the same total. Who won the tournament if Branimir finished ahead of Andrea?
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Answer: D — Doris
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Hint 1 of 2
Use that all four ranks add to 1+2+3+4 = 10.
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Hint 2 of 2
From A+B+D = 6 find Celestin's rank, and from B+C = 6 find Branimir's, then place the rest.
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Approach: sum constraint
- Ranks 1–4 total 10. A + B + D = 6 means Celestin's rank C = 4.
- B + C = 6 with C = 4 gives Branimir B = 2.
- Remaining ranks 1 and 3 go to Andrea and Doris; Branimir(2) beat Andrea, so Andrea = 3 and Doris = 1.
- Rank 1 wins, so Doris won — answer D.
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