{"status": "success", "data": {"description_md": "Every card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three colors - red, blue, or green. Furthermore, each color is applied in one of three shades - light, medium, or dark. The deck has 27 cards, with every shape-color-shade combination represented. A set of three cards from the deck is called complementary if all of the following statements are true:<br><br>i. Either each of the three cards has a different shape or all three of the card have the same shape.<br>ii. Either each of the three cards has a different color or all three of the cards have the same color.<br>iii. Either each of the three cards has a different shade or all three of the cards have the same shade.<br><br>How many different complementary three-card sets are there?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Every card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three colors - red, blue, or green. Furthermore, each color is applied in one of three shades - light, medium, or dark. The deck has 27 cards, with every shape-color-shade combination represented. A set of three cards from the deck is called complementary if all of the following statements are true:<br/><br/>i. Either each of the three cards has a different shape or all three of the card have the same shape.<br/>ii. Either each of the three cards has a different color or all three of the cards have the same color.<br/>iii. Either each of the three cards has a different shade or all three of the cards have the same shade.<br/><br/>How many different complementary three-card sets are there?</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "1997 AIME Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/97_aime_p11", "prev": "/problem/97_aime_p09"}}