document.write( "Question 1026255: there are coconuts in a basket. when they are removed seven at a time six remains at the end,when they removed six at a time, five remains, five at a time four remains and so on till two at a time and one remains. what is the smallest number of coconuts in the basket originally? \n" ); document.write( "

Algebra.Com's Answer #641496 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "there are coconuts in a basket. when they are removed seven at a time six remains at the end, when they removed six at a time, five remains, five at a time four remains and so on till two at a time and one remains. what is the smallest number of coconuts in the basket originally?
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document.write( "Let me re-formulate the problem in this, equivalent way:\r\n" );
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document.write( "   There are coconuts in a basket. \r\n" );
document.write( "   When they are arranged by groups of 7, six coconuts remain in the last group. \r\n" );
document.write( "   When they are arranged by groups of 6, five coconuts remain in the last group.   \r\n" );
document.write( "   When they are arranged by groups of 5, four coconuts remain in the last group.   \r\n" );
document.write( "   And so on till two coconuts in groups and 1 as a remainder. \r\n" );
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document.write( "   What is the smallest number of coconuts in the basket originally?\r\n" );
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document.write( "Solution\r\n" );
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document.write( "Let n be the smallest number of coconuts in the basket originally.\r\n" );
document.write( "Add one coconut. You will have (n+1) coconuts.\r\n" );
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document.write( "Then (n+1) is divisible by 7 without a remainder,\r\n" );
document.write( "           is divisible by 6 without a remainder,\r\n" );
document.write( "           is divisible by 5 without a remainder,\r\n" );
document.write( "           is divisible by 4 without a remainder,\r\n" );
document.write( "           is divisible by 3 without a remainder,\r\n" );
document.write( "           is divisible by 2 without a remainder.\r\n" );
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document.write( "Thus (n+1) is divisible by  = 420 without a remainder.\r\n" );
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document.write( "The smallest such a number is n+1 = 420.\r\n" );
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document.write( "Hence, n = 419.\r\n" );
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