2347 /www/nrich/html/content/04/weekly/prob23/ 1 2010-09-30T13:59:20 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>In how many whole numbers between 100 and 999 is the middle digit equal to the sum of the other two digits?</p> <p> </p> <p>If you liked this problem, <a href="http://nrich.maths.org/public/viewer.php?obj_id=5865">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>Consider numbers whose fist digit is 1. Looking at each possible value for the second digit we find 9 such numbers.</p> <p>110, 121, 132, 143, 154, 165, 176, 187, 198.</p> <p>Similarly there are 8 numbers starting with 2; 7 numbers starting with 3...</p> <p>Lastly there is only one number starting with 9: 990.</p> <p>Hence the total is 9+8+7+6+5+4+3+2+1 = 45.</p> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>Consider numbers whose fist digit is 1. Looking at each possible value for the second digit we find 9 such numbers.</p> <p>110, 121, 132, 143, 154, 165, 176, 187, 198.</p> <p>Similarly there are 8 numbers starting with 2; 7 numbers starting with 3...</p> <p>Lastly there is only one number starting with 9: 990.</p> <p>Hence the total is 9+8+7+6+5+4+3+2+1 = 45.</p> </mdoxml> 2 3 0 0 0 0 0 Weekly Problem 53 - 2011 Secondary Mapping Document Place value, ordering and rounding LS