IBM Research | Ponder This | January 2011 solutions

# Ponder This

## January 2011

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The rational fraction 204193/178481in base-8 is 0.(11160440223411004470220), where the 0.(xyz) notation means 0.xyzxyzxyzxyz...

The 2**-40 changes the 14th digit, so the winning starting numbers are {1,2,3,13} and {1,2,3,13,14}+23*k for k>0.
From this, we get 13 letters that must not appear (A, B, C, J, K, L, M, U, V, W, X, Y, Z); four that must appear (D, I, N, T); and several constraints on the rest.
We can build several two-word phrases with six and four letters in the words, respectively, that satisfy all these conditions, such as "Hidden Tree", "Things Done", "Prison Diet", and even possible names for the teacher and student ("Dennis Roth" and "Ginger Todd" - thanks Chuck Carroll for this suggestion). The phrase that we chose, however, as almost all of you guessed, is simply "Ponder This".

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