The idea of speculating given a set of constraints is such a common notion that you might want to try it again in a different setting.
In this puzzle, you are given several groups of 2 to 9 letters. Each group encodes an ascending consecutive run of numbers, e.g. 2, 3, 4, 5. In the simplest version of this puzzle, each letter encodes a single number between 1 and 9. Your job is to find the encoding.
Assume this simplest encoding. Find the single number represented by each letter. Suppose the groups you see are:
GDF IHEC DFBIH FBIHECA HE FBIH IHE FBIHEC BIHE EC FB
Because each group represents an ascending run of numbers, FBIHEC represents a subsequence of the numbers of FBIHECA, so it doesn’t tell anything new. In general, we don’t care about any groups that are subsequences of others. This leaves us with GDF, DFBIH, and FBIHECA. Putting the first and third of these together, you get GDFBIHECA. So, G = 1, D = 2, …, A = 9.
That was just a warm-up. Now consider the case where a letter can represent two numbers.
Can you figure out which (up to) two numbers each letter represents?
EDHFHI FDBFHI ACBEDHG BFEBGDI HFD IEDH EEBGH EHG HGH FEBGH FEBF CBEEBF IEDBFDG CIFD ACBFEB EEB CBEEHGDG ED ACIFEHG FEBG CIFE CIEEH BFDH
For those who are gluttons for punishment, what are the up to three encodings for each letter given this list of groups?
ABBDH DCHGEBF AFCFAE ADCFAEG EBFG IAAGIB ADCI HBBDB IHBID FCFGAII DCIHEI FCHGBG AFCFA EIDG DCFGAB ABBDB FCIH GEI HAE AI CFGAGF DCIAE EIDB BIIB AEB BIDH EBD AABF EGD EDCIHE CIHBBI CFABB AIF GDB HBID GIH EFCI HGAG HABG FCI BIFG DCHGBBDH FCHABI FGEGF ABID BIFH CFHEB
Can you figure out which (up to) two numbers each letter represents?
Here is the solution for the case in which a single letter may represent up to two letters.
A is 1; B is 3 or 6; C is 2; D is 5 or 8; E is 4 or 5; F is 4 or 7; G is 7 or 9; H is 6 or 8; I is 3 or 9.
For those who are gluttons for punishment, what are the up to three encodings for each letter given this list of groups?
Here is a solution in the case when each single letter can represent up to three letters.
A is 1, 5, or 6; B is 6, 7, or 9; C is 3; D is 2 or 8; E is 1 or 6; F is 2, 4, or 8; G is 5, 7, or 9; H is 4, 5 or 9; I is 4, 7, or 8.