IBM Ponder This #177 · January 2013

The following six permutations of the letters EISH

EISH
    HESI
    IEHS
    HISE
    SEHI
    SIHE

satisfy that for every three letters, and every order, there exists a permutation in which these three letters appear in this order. For example, SHE appears in the last line and HIS appears in the fourth line.

Find 13 permutations of the letters ABCEFHIJLMNPQTVXYZ which satisfy the same condition: for every three letters and every one of their six possible orders, there exists at least one permutation in which the letters appear in this order.

A bonus question: What is special about this set of letters?

Solution

Best opened after a real attempt

To be added.