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In an archery contest, the judge decides some target score X, where X can be any number from 1 to 30. Then the participant fires multiple arrows at a target, one after the other; till he precisely achieves a total score of X. For each arrow, hitting the center "bull's eye" of the target is worth 10 points; and the surrounding rings are worth 6, 3 and 1 points respectively. (The participant is allowed to hit the same region more than once). What is the minimum number of arrows that will surely be enough, regardless of what X is?

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#### Puzzle No. 25

*Posted on 17 June 2016*In an archery contest, the judge decides some target score X, where X can be any number from 1 to 30. Then the participant fires multiple arrows at a target, one after the other; till he precisely achieves a total score of X. For each arrow, hitting the center "bull's eye" of the target is worth 10 points; and the surrounding rings are worth 6, 3 and 1 points respectively. (The participant is allowed to hit the same region more than once). What is the minimum number of arrows that will surely be enough, regardless of what X is?

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