For today's Daily Magic Spell Discussion, we will look at the problem given on January 9, 2017.
Problem: Let $N$ be the largest seven-digit palindrome that can be constructed from the digits $1,2,3,4,5,6,7$ (repeats are allowed) such that the sum of every pair of consecutive digits is a prime number. What is the number $N$?
Solution: The largest number is $7676767$ since $7+6 = 6+7=13$ is the largest prime you can get.
To approach this question, note that the largest prime number that you can add together by two digits is $7$ and $6$. Some students may have attempted to try and brute forced methods so that two consecutive digits add to a prime number. Some students may not realize that this can be done by swapping the digits. Because of this, their answers are marked incorrect.
Some students may also approach the question without realizing that they can repeat digits.Because of this, students would respond $7652341$. This is achieved by starting with $7$, asking if adding $6$ will yield a prime number. If so, move onto the next digit. If not, ask if $4$ adds up to a prime number.
If you have any other approaches to tackling this question, please do not hesitate to respond to the forum discussion. We would love to offer you feedback!