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Ponder This

July 2011

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We can solve the problem for 81 = 3^4 students using linear codes. Write each student as a 4-digit number in base 3, and let him eat the scalar multiplication of his number with the following constants:

(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1), (0,0,1,1), (0,0,1,2), (1,1,0,0), (1,2,0,0), (0,1,0,1), (0,1,0,2), (1,0,1,0), (1,0,2,0), (1,1,1,1), (1,1,2,2)

Click here to see the format we requested

And click here to see another representation sent to us by Gale Greenlee.

14 is the smallest number of days we found with a solution, yet we can prove a lower bound of 10. We leave this gap as an open question for our readers.

This month James Dow Allen solved the unasked bonus question: Why did we ask for lines 80 characters in length when the solution lends itself to 81? Of course, we did it to make the solution a little less obvious, but also to honor the 80-character-wide IBM punched card.

For more information see http://www.ibm.com/ibm100/us/en/icons/punchcar.

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Here it is in the format we requested:

ABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCABCAB

AAABBBCCCAAABBBCCCAAABBBCCCAAABBBCCCAAABBBCCCAAABBBCCCAAABBBCCCAAABBBCCCAAABBBCC

AAAAAAAAABBBBBBBBBCCCCCCCCCAAAAAAAAABBBBBBBBBCCCCCCCCCAAAAAAAAABBBBBBBBBCCCCCCCC

AAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCC

AAAAAAAAABBBBBBBBBCCCCCCCCCBBBBBBBBBCCCCCCCCCAAAAAAAAACCCCCCCCCAAAAAAAAABBBBBBBB

AAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCCCCCAAAAAAAA

ABCBCACABABCBCACABABCBCACABABCBCACABABCBCACABABCBCACABABCBCACABABCBCACABABCBCACA

ABCCABBCAABCCABBCAABCCABBCAABCCABBCAABCCABBCAABCCABBCAABCCABBCAABCCABBCAABCCABBC

AAABBBCCCAAABBBCCCAAABBBCCCBBBCCCAAABBBCCCAAABBBCCCAAACCCAAABBBCCCAAABBBCCCAAABB

AAABBBCCCAAABBBCCCAAABBBCCCCCCAAABBBCCCAAABBBCCCAAABBBBBBCCCAAABBBCCCAAABBBCCCAA

ABCABCABCBCABCABCACABCABCABABCABCABCBCABCABCACABCABCABABCABCABCBCABCABCACABCABCA

ABCABCABCCABCABCABBCABCABCAABCABCABCCABCABCABBCABCABCAABCABCABCCABCABCABBCABCABC

ABCBCACABBCACABABCCABABCBCABCACABABCCABABCBCAABCBCACABCABABCBCAABCBCACABBCACABAB

ABCBCACABCABABCBCABCACABABCCABABCBCABCACABABCABCBCACABBCACABABCABCBCACABCABABCBC

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Representation sent to us by Gale Greenlee

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com