document.write( "Question 1146503: There is quite a pile of playing cards sitting at my house. A discovery I have
\n" ); document.write( "made is as follows. If all the cards are dealt to all the people, then:\r
\n" ); document.write( "\n" ); document.write( "if 2 people are playing cards one card will be left over.
\n" ); document.write( "if 3 people are playing cards 2 cards will be left over.
\n" ); document.write( " if 4 people are playing cards 3 cards will be left over.
\n" ); document.write( "if 5 people are playing cards. 4 cards will be left over.
\n" ); document.write( "if 6 people are playing cards 5 cards will be left over.
\n" ); document.write( "If seven people are playing cards no cards will be left over.
\n" ); document.write( "if I have the minimum amount of cards to satisfy the above conditions how many
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Algebra.Com's Answer #768354 by ikleyn(52855) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "     There is a set of cards.\r\n" );
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document.write( "     If they are distributed equally between 2 persons, 1 card  is  leftover.\r\n" );
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document.write( "     If they are distributed equally between 3 persons, 2 cards are leftover.\r\n" );
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document.write( "     If they are distributed equally between 4 persons, 3 cards are leftover.\r\n" );
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document.write( "     If they are distributed equally between 5 persons, 4 cards are leftover.\r\n" );
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document.write( "     If they are distributed equally between 6 persons, 5 cards are leftover.\r\n" );
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document.write( "     If they are distributed equally between 7 persons, NO cards are leftover.\r\n" );
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document.write( "     Find the minimum amount of cards to satisfy the above conditions.\r\n" );
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document.write( "Let N be the number under the question.\r\n" );
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document.write( "Add (mentally) 1 card to the set of cards. In other words, consider the number N+1.\r\n" );
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document.write( "Then it is divisible by 2; by 3; by 4; by 5 and by 6.\r\n" );
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document.write( "The minimal such a number is  60.\r\n" );
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document.write( "Check then, if  N-1 = (60-1) = 59 is divisble by 7.   ----- It is not divisible.\r\n" );
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document.write( "Next number to try is 60*2 = 120.\r\n" );
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document.write( "Check if 120-1 = 119 is divisible by 7.  ----- You are LUCKY: it is (!).\r\n" );
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document.write( "So the answer to the problem is  N = 119.\r\n" );
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\n" ); document.write( "\n" ); document.write( " ( ! ) S O L V E D ( ! )\r
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\n" ); document.write( "\n" ); document.write( "It is a standard problem of a school Math circle level (typically, for children starting from 5-th or 6-th grade).\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Find there a lot of similar problems, solved and explained to you.\r
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\n" ); document.write( "\n" ); document.write( "When children attend such Math circles and solve there such problems under guidance of devoted and enthusiastic teachers,
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\n" ); document.write( "\n" ); document.write( "Then there is also a chance that they will pass this enthusiasm and the way of thinking to their own children
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