Rearrange the key caps of the 1 through 9 on a numeric keypad so that no cap is on its correct key, in such a manner that each of the three rows forms a 3-digit perfect square.

  
789
456
123
  

324 and 361 are only 3 digit perfect squares having digit "3"

576,729,784 are only 3 digit perfect squares having digit "7"

324 only goes with 576, leaving digit 1,8,9 - no sqare possible

so 361 is one of the rows.

841, 784 and 324 are only squares with digit "4", 324 is disqualified(step 1). remains 841, 784. Using both numbers leaves bahind 579 and 529 respectively. out of which 529 is perfect square.

hence, 361, 784, 529 --- there are 6 ways to put these number but 784 cant be a top and 529 cant be at bottom/top.

so only one way: 316, 529, 784

Posted by Ritesh on 2011-05-20 21:29:34