document.write( "Question 1132815: Rustam likes multiples of 5. For his RSM project he makes up numbers such that any two of the digits of any of his numbers, when put next to each other in some order, make a two-digit multiple of 5. His teacher calls such numbers Rustam’s numbers. For example, the numbers 51 and 502 are Rustam’s numbers, but the numbers 300 and 2018 are not. How many different three-digit Rustam’s numbers with none of the digits greater than 5 are there?
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Algebra.Com's Answer #749954 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "These 3-digit numbers are such that they\r\n" );
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document.write( "    - EITHER contain at least two digits 5,        (category 1)\r\n" );
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document.write( "    - OR     contain both the digits  5 and 0,     (category 2)\r\n" );
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document.write( "    - OR     contain two digits 0.                 (category 3).\r\n" );
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document.write( "In category 1  we have 13 numbers\r\n" );
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document.write( "    155, 255, 355, 455, 555,\r\n" );
document.write( "    515, 525, 535, 545, \r\n" );
document.write( "    551, 552, 553, 554.\r\n" );
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document.write( "In category 2 we have 18 numbers\r\n" );
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document.write( "    105, 205, 305, 405, 505,\r\n" );
document.write( "    150, 250, 350, 450, 550,\r\n" );
document.write( "    510, 520, 530, 540,\r\n" );
document.write( "    501, 502, 503, 504.\r\n" );
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document.write( "In category 3 we have 5 numbers.\r\n" );
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document.write( "    100, 200, 300, 400, 500.\r\n" );
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document.write( "In all, there are  13 + 18 + 5 = 36 such numbers.\r\n" );
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document.write( "It may happen that I missed something, but the idea is clear.\r\n" );
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document.write( "This hint is  EITHER  the full solution  OR  a good push for those who study at RSM (Russian School of Mathematics).\r\n" );
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document.write( "P.S.  If you think that the numbers of category 3  should not be included to the set of R-numbers  \r\n" );
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document.write( "      (in this part your definition is not certain), then exclude them . . . \r\n" );
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