On a Unit Fraction Question of Erdos and Graham

On page 161 of Guy's excellent book "Unsolved Problems in Number
Theory" (2nd Ed) it discusses expressing 1 as the sum of t distinct
unit fractions.  Letting m(t) denote the smallest possible maximum
denominator in such a sum, he notes that m(3)=6 and m(4)=12.  These
follow from the optimum 3-term and 4-term expressions

              1  =  1/2 + 1/3 + 1/6

              1  =  1/2 + 1/4 + 1/6 + 1/12

However, the book goes on to say that m(12)=120.  Is this just a typo?
If I've interpreted the definition of m(t) correctly it seems to me
m(12) cannot be greater than 30.  Here's a table of the optimum
expansions for t=3 to 12:

      t             denominators of optimum expansion
     ---       -----------------------------------------------
      3         2   3   6
      4         2   4   6  12
      5         2   4  10  12  15
      6         3   4   6  10  12  15
      7         3   4   9  10  12  15  18
      8         3   5   9  10  12  15  18  20
      9         4   5   8   9  10  15  18  20  24
     10         5   6   8   9  10  12  15  18  20  24
     11         5   6   8   9  10  15  18  20  21  24  28
     12         6   7   8   9  10  14  15  18  20  24  28  30

I'm not actually certain the above expansion for t=12 is optimum, but
it proves that the maximum denominator of the optiumum expansion is
certainly no greater than 30.  Am I missing something?


Richard Guy wrote:
 This is indeed an error, and one which has been there since the 
 first edition, 15 years ago.  I must have miscopied or misunderstood 
 it from Erd"os or Graham.  It's surprising that no-one has pointed it 
 out earlier.  I keep an updating file for UPINT and your message will 
 be incorporated.