Enigma 1068: Triangular Fibonacci squares
2 April 2018
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From New Scientist #2224, 5th February 2000 [link]
Harry, Tom and I were trying to find a 3-digit perfect square, a 3-digit triangular number and a 3-digit Fibonacci number that between them used nine different digits. (Triangular numbers are those that fit the formula n(n+1)/2; in the Fibonacci sequence the first two terms are 1 and 1, and every succeeding term is the sum of the previous two terms). We each found a valid solution and we each created a second valid solution by retaining two of the numbers of our first solution but changing the other one. Our six solutions were all different.
List in ascending order the numbers in the solution that none of us found.