category stringclasses 6
values | contest stringclasses 283
values | link stringlengths 21 100 | name stringlengths 3 83 | source stringlengths 17 36 | problem stringlengths 2 129 ⌀ | problem_html stringlengths 86 41.5k | solution_1 stringlengths 515 448k ⌀ | solution_2 stringlengths 513 217k ⌀ | solution_3 stringlengths 516 235k ⌀ | solution_4 stringlengths 518 186k ⌀ | solution_5 stringlengths 520 129k ⌀ | which stringlengths 1 12 ⌀ |
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international_contests | IMO Shortlist | /community/c3964_2013_imo_shortlist | 2013 IMO Shortlist | /community/c6h597130p3543398 | IMO Shortlist 2013 Combinatorics #3 | <div class="cmty-post-html">
<div>
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A crazy physicist discovered a new kind of particle wich he called an imon, after some of them mysteriously appeared in his lab. Some pairs of imons in the lab can be entangled, and each imon can participate in many entanglement relations. The physicist has found a way to pe... | [23, '<div class="cmty-post-html">\n <div>\n </div>\n Consider the graph\n <img alt="$G$" class="latex" height="12" src="//latex.artofproblemsolving.com/6/e/2/6e28ce12d49d39f160d5a0ef54077fc98e4b9d2b.png" width="14"/>\n with imons as vertices and an edge between two vertices if the imons are entangled.\n <br/>\n <br/>\... | [22, '<div class="cmty-post-html">\n <div>\n </div>\n We\'ll go by strong induction on the number of vertices\n <span style="white-space:nowrap;">\n <img alt="$n$" class="latex" height="8" src="//latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10"/>\n .\n </span>\n Base case\n... | [6, '<div class="cmty-post-html">\n <div>\n </div>\n Let\n <img alt="$n$" class="latex" height="8" src="//latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10"/>\n be the number of imons in the lab.\n <br/>\n <br/>\n We induct on\n <img alt="$n.$" class="latex" height="8" src="//l... | [6, '<div class="cmty-post-html">\n <div>\n </div>\n <div class="bbcode_quote">\n <div class="bbcode_quote_head">\n lyukhson wrote:\n </div>\n <div class="bbcode_quote_body">\n A crazy physicist discovered a new kind of particle wich he called an imon, after some of them mysteriously appeared in his lab. Some pa... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n Represent the imons and entanglements by a graph, in which imons are vertices and entanglements are edges.\n <br/>\n <br/>\n Call operation (ii) "stacking." For a graph\n <img alt="$G$" class="latex" height="12" src="//latex.artofproblemsolving.com/6/e/2/6e28ce12d49d... | C3 |
international_contests | IMO Shortlist | /community/c3964_2013_imo_shortlist | 2013 IMO Shortlist | /community/c6h597131p3543403 | IMO Shortlist 2013 Combinatorics #4 | <div class="cmty-post-html">
<div>
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Let
<img alt="$n$" class="latex" height="8" src="//latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10"/>
be a positive integer, and let
<img alt="$A$" class="latex" height="13" src="//latex.artofproblemsolving.com/0/1/9/019e9892786... | [8, '<div class="cmty-post-html">\n <div>\n </div>\n Assume that there are\n <img alt="$x$" class="latex" height="8" src="//latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="10"/>\n different parts,\n <img alt="$a_{1},a_{2},...,a_{x}$" class="latex" height="11" src="//latex.artofp... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n Easily killed by this\n <img alt=";)" class="bbcode_smiley" height="20" src="/assets/images/smilies/wink.gif" title=";)" width="20"/>\n <a class="cmty-hide-heading" href="#" onclick="$(this).next().toggle();$(this).toggleClass(\'cmty-hide-open\');return false;">\n L... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n <div class="bbcode_quote">\n <div class="bbcode_quote_head">\n lyukhson wrote:\n </div>\n <div class="bbcode_quote_body">\n Let\n <img alt="$n$" class="latex" height="8" src="//latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png"... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n Suppose we have an optimal partition\n <img alt="\\[ n = e_1 \\cdot a_1 + \\dots + e_m \\cdot a_m. \\]" class="latexcenter" height="13" src="//latex.artofproblemsolving.com/1/9/c/19ca11a59e124c7b5b6f586c9fdccb279f16e9b2.png" width="206"/>\n In order for this to be o... | [3, '<div class="cmty-post-html">\n <div>\n </div>\n Suppose the distinct elements of the optimal\n <span style="white-space:pre;">\n <img alt="$A$" class="latex" height="13" src="//latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="13"/>\n -\n </span>\n partition are\n <span sty... | C4 |
team_selection_test | Peru IMO TST | /community/c875049_2014_peru_imo_tst | 2014 Peru IMO TST | /community/c6h597131p3543403 | IMO Shortlist 2013 Combinatorics #4 | <div class="cmty-post-html">
<div>
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Let
<img alt="$n$" class="latex" height="8" src="//latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10"/>
be a positive integer, and let
<img alt="$A$" class="latex" height="13" src="//latex.artofproblemsolving.com/0/1/9/019e9892786... | [8, '<div class="cmty-post-html">\n <div>\n </div>\n Assume that there are\n <img alt="$x$" class="latex" height="8" src="//latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="10"/>\n different parts,\n <img alt="$a_{1},a_{2},...,a_{x}$" class="latex" height="11" src="//latex.artofp... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n Easily killed by this\n <img alt=";)" class="bbcode_smiley" height="20" src="/assets/images/smilies/wink.gif" title=";)" width="20"/>\n <a class="cmty-hide-heading" href="#" onclick="$(this).next().toggle();$(this).toggleClass(\'cmty-hide-open\');return false;">\n L... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n <div class="bbcode_quote">\n <div class="bbcode_quote_head">\n lyukhson wrote:\n </div>\n <div class="bbcode_quote_body">\n Let\n <img alt="$n$" class="latex" height="8" src="//latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png"... | [4, '<div class="cmty-post-html">\n <div>\n </div>\n Suppose we have an optimal partition\n <img alt="\\[ n = e_1 \\cdot a_1 + \\dots + e_m \\cdot a_m. \\]" class="latexcenter" height="13" src="//latex.artofproblemsolving.com/1/9/c/19ca11a59e124c7b5b6f586c9fdccb279f16e9b2.png" width="206"/>\n In order for this to be o... | [3, '<div class="cmty-post-html">\n <div>\n </div>\n Suppose the distinct elements of the optimal\n <span style="white-space:pre;">\n <img alt="$A$" class="latex" height="13" src="//latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="13"/>\n -\n </span>\n partition are\n <span sty... | 16 |
international_contests | IMO Shortlist | /community/c3964_2013_imo_shortlist | 2013 IMO Shortlist | /community/c6h597133p3543427 | IMO Shortlist 2013 Combinatorics #5 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n Let\n <img alt=\"$r$\" class=\"latex\" height=\"8(...TRUNCATED) | "[5, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <a class=\"cmty-hide-heading\" href=\"#\"(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n A similar (but much shorter, it seems) ar(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n The same idea, but a little bit different(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <div class=\"bbcode_quote\">\\n <div cla(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Setting\\n <img alt=\"$s=0$\" class=\"lat(...TRUNCATED) | C5 |
national_and_regional_contests | Taiwan Contests | /community/c3395_tst_round_2 | TST Round 2 | /community/c6h597133p3543427 | IMO Shortlist 2013 Combinatorics #5 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n Let\n <img alt=\"$r$\" class=\"latex\" height=\"8(...TRUNCATED) | "[5, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <a class=\"cmty-hide-heading\" href=\"#\"(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n A similar (but much shorter, it seems) ar(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n The same idea, but a little bit different(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <div class=\"bbcode_quote\">\\n <div cla(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Setting\\n <img alt=\"$s=0$\" class=\"lat(...TRUNCATED) | 2 |
team_selection_test | India IMO Training Camp | /community/c5008_2014_india_imo_training_camp | 2014 India IMO Training Camp | /community/c6h597133p3543427 | IMO Shortlist 2013 Combinatorics #5 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n Let\n <img alt=\"$r$\" class=\"latex\" height=\"8(...TRUNCATED) | "[5, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <a class=\"cmty-hide-heading\" href=\"#\"(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n A similar (but much shorter, it seems) ar(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n The same idea, but a little bit different(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <div class=\"bbcode_quote\">\\n <div cla(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Setting\\n <img alt=\"$s=0$\" class=\"lat(...TRUNCATED) | 3 |
international_contests | IMO Shortlist | /community/c3964_2013_imo_shortlist | 2013 IMO Shortlist | /community/c6h597136p3543443 | IMO Shortlist 2013 Combinatorics #6 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n In some country several pairs of cities are conne(...TRUNCATED) | "[9, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Personally, aside from C1 I found this to(...TRUNCATED) | "[8, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n My first ISL!! Anyways, a straightforward(...TRUNCATED) | "[5, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n The bound is tight, by the way. For insta(...TRUNCATED) | "[3, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n This is a lovely problem, but an absolute(...TRUNCATED) | "[2, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Hmm, not sure what I was doing all those (...TRUNCATED) | C6 |
international_contests | IMO Shortlist | /community/c3964_2013_imo_shortlist | 2013 IMO Shortlist | /community/c6h597140p3543469 | IMO Shortlist 2013 Combinatorics #8 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n Players\n <img alt=\"$A$\" class=\"latex\" height(...TRUNCATED) | "[14, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n I don\\'t know what is wrong with this g(...TRUNCATED) | "[3, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Huh?\\n <img alt=\"$A$\" class=\"latex\" (...TRUNCATED) | "[3, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n We discussed this solution during Canadia(...TRUNCATED) | "[3, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <b>\\n SOLVED WITH MY IDOLS\\n <a class(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <div class=\"bbcode_quote\">\\n <div cla(...TRUNCATED) | C8 |
international_contests | IMO Shortlist | /community/c3964_2013_imo_shortlist | 2013 IMO Shortlist | /community/c6h597143p3543487 | IMO Shortlist 2013 Geometry #2 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n Let\n <img alt=\"$\\omega$\" class=\"latex\" heig(...TRUNCATED) | "[6, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <b>\\n Claim:\\n </b>\\n <img alt=\"$AMX(...TRUNCATED) | "[4, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <a class=\"cmty-hide-heading\" href=\"#\"(...TRUNCATED) | "[4, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n First we will prove that\\n <span style=\(...TRUNCATED) | "[3, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Let\\n <img alt=\"$ O $\" class=\"latex\"(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <img alt=\\'[asy]\\n /* Geogebra to Asymp(...TRUNCATED) | G2 |
team_selection_test | France TST | /community/c5355_2014_france_team_selection_test | 2014 France TST | /community/c6h597143p3543487 | IMO Shortlist 2013 Geometry #2 | "<div class=\"cmty-post-html\">\n <div>\n </div>\n Let\n <img alt=\"$\\omega$\" class=\"latex\" heig(...TRUNCATED) | "[6, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <b>\\n Claim:\\n </b>\\n <img alt=\"$AMX(...TRUNCATED) | "[4, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <a class=\"cmty-hide-heading\" href=\"#\"(...TRUNCATED) | "[4, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n First we will prove that\\n <span style=\(...TRUNCATED) | "[3, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n Let\\n <img alt=\"$ O $\" class=\"latex\"(...TRUNCATED) | "[1, '<div class=\"cmty-post-html\">\\n <div>\\n </div>\\n <img alt=\\'[asy]\\n /* Geogebra to Asymp(...TRUNCATED) | 5 |
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