2344 /www/nrich/html/content/04/weekly/prob20/ 1 2010-08-07T12:23:31 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>The pattern 123451234512345... is continued to form a 2000 digit number. What is the sum of all 2000 digits?</p> <p> </p> <p>If you liked this problem, <a href="http://nrich.maths.org/2278">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>The number may be divided up into 400 blocks of '12345'. The sum of the digits in each block is 15 and there are 400 blocks. Hence the sum of all 2000 digits is 400 x 15 = 6000.</p> <p>Alternatively, the mean of each group of five digits is 3 and so the mean of the digits making up the number is 3. Therefore the sum is 2000x3 = 6000.</p> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>The number may be divided up into 400 blocks of '12345'. The sum of the digits in each block is 15 and there are 400 blocks. Hence the sum of all 2000 digits is 400 x 15 = 6000.</p> <p>Alternatively, the mean of each group of five digits is 3 and so the mean of the digits making up the number is 3. Therefore the sum is 2000x3 = 6000.</p> </mdoxml> 2 3 0 0 0 0 0 Weekly Problem 50 - 2011