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IMSO 2009 Mathematics Contest in Taiwan – Short Answer Question 11

IMSO Maths · IMSO 2009 Mathematics Contest in Taiwan – Short Answer

Question 11

A combination lock on a safe needs a six-letter sequence to open it, made from A, B, C, D, E, F with none used twice. Here are three guesses:

| Guess | 1 | 2 | 3 | 4 | 5 | 6 |
| --- | --- | --- | --- | --- | --- | --- |
| FIRST | C | B | A | D | F | E |
| SECOND | A | E | D | C | B | F |
| THIRD | E | D | F | A | C | B |

In the FIRST guess only ONE letter is in its correct place. In the SECOND guess only TWO letters are correctly placed, and those two positions are not next to each other. In the THIRD guess only THREE letters are correctly placed. Each of the six letters is in its correct place once across the guesses. What is the correct combination?