{"status": "success", "data": {"description_md": "A new language uses only the letters A, B, C, D, and E. The letters A and E are called *vowels*, while the letters B, C and D are called *consonants*. A sequence of letters is called a *word* if it does not include the same letter twice in a row, and it does not include two vowels in a row. How many words are there in this language that are 10 letters long and that begin with a vowel?\n\n$\\text{(A)}\\ 199\\,680\\qquad\\text{(B)}\\ 199\\,968\\qquad\\text{(C)}\\ 199\\,584\\qquad\\text{(D)}\\ 199\\,872\\qquad\\text{(E)}\\ 199\\,776$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>A new language uses only the letters A, B, C, D, and E. The letters A and E are called *vowels*, while the letters B, C and D are called *consonants*. A sequence of letters is called a *word* if it does not include the same letter twice in a row, and it does not include two vowels in a row. How many words are there in this language that are 10 letters long and that begin with a vowel?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 199\\,680\\qquad\\text{(B)}\\ 199\\,968\\qquad\\text{(C)}\\ 199\\,584\\qquad\\text{(D)}\\ 199\\,872\\qquad\\text{(E)}\\ 199\\,776</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2016 Cayley Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/16_cayley_p24"}}