A Six-Pointed Star

b  c d  e
 f     g
h  i j  k
  1. Place the numbers 1 to 12 in the 12 locations on the six-pointed star, such that each of the six lines of four numbers has the same sum and the sum of the six points of the star has the same sum as the lines.
  2. Can you find an arrangement for which the six lines and the set of six star-points produce seven consecutive sums?

Source: 1. Henry Ernest Dudeny, 536 Curious Problems & Puzzles, #394. 2. Original.

Mail to Ken