Problem 098

[laogui]

(3) CONSIDERABLE ABCDEEILNORS 11
(3) RELATIONSHIP AEHIILNOPRST 11
(3) RESPONSIBILITY BEIIILNOPRSSTY 11
Problem statement does not specify what to do with words having more than 10 distinct letters (of which there are three). It should, wouldn't you agree?

[jaap]

(3) CONSIDERABLE ABCDEEILNORS 11
(3) RELATIONSHIP AEHIILNOPRST 11
(3) RESPONSIBILITY BEIIILNOPRSSTY 11
Problem statement does not specify what to do with words having more than 10 distinct letters (of which there are three). It should, wouldn't you agree?

There is no need, as they don't form any anagram pairs.

[drwhat]

Even if they did form an anagram pair, the problem states that no two letters can be assigned the same digit. All words that have 11+ distinct letters, MUST have 2 letters assigned the same digit, ergo all such words are ruled out of the solution.

[laogui]

@drwhat:Even if they did form an anagram pair, the problem states that no two letters can be assigned the same digit. NO IT DOESN'T - it says no two DIFFERENT letters
The problem should not provide 11 different letter words or should stipulate to exclude them since they cannot be assigned digits 0-9

[laogui]

@jaap so in other words, near enough is good enough. Problem statements should be rigorous, not near enough, and I assure you Euler would have strongly disagreed. The problem provides data which breaches rules or is exceptional. Do you program without catering for exceptions? The problem statements should be precise.

[DJohn]

The problem statement looks sufficiently rigorous to me - as far as it's possible for it to be rigorous when written in English. I don't think Project Euler would enjoy quite the same level of popularity if all problems were written in Coq.

We are asked to find pairs of words with a particular property - there is an assignment of digits to letters which turns each word into a square, with some restrictions on that assignment. Some pairs are ruled out because there is no assignment of digits that gives a square for each word. Some pairs are ruled out because there is no valid assignment of digits at all.

The restrictions are that whatever the assignment of digits is, neither word can start with zero, and "neither may a different letter have the same digital value as another letter." If we're assigning digit x to letter y, we can't assign digit x to letter z as well (if y and z are different letters). You might be thrown by it introducing the "different digit" before the thing that it's different from, but that's not an uncommon construction in Mathematical English.