Enigmatics |
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Posted on: Friday 25/1, 2008; 7:04 PM Constuct a list of all perfect squares with 1, 2, 3, or 4 digits, and then split each square into its constituent digits. Remove all cases where the squares contain repeated digits, then split the resulting list into 4 sublists corresponding to 1-digit, 2-digit, 3-digit, and 4-digit squares.
Construct a list of partitions of 10 formed from the integers 1, 2, 3, and 4 that can be used as indices to pick candidate lists of 4 sublists from the above list, which are thus guaranteed to have a total of exactly 10 digits in them. The condition that the digits are different has not yet been applied here.
Construct a list of all of the candidate lists of 4 sublists.
Pick out the cases in which all of the digits are different. There are only 4 such cases. Pick out Peter and Quentin's cases, which must have exactly 2 squares in common. Remove Peter and Quentin's cases to leave 2 cases yet to be assigned. Pick out Rose's case, which must not have any squares in common with either Peter or Quentin's cases. |
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