Questions about grandpa (with chess puzzle clue)

Question

Here are two questions about my grandpa Herb, along with parts of the answers. Can you complete the answers to both questions?

Q: Who was grandpa Herb's favorite president?

A: he gOeS By ...

Q: What did grandpa Herb buy at the store on March 26, 1987?

A: A smALL RIce

Here is a helpful clue, in the form of a chess puzzle, to help you answer the question. I hope it helps.

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It's been a few days, so I wanted to some hints in case anyone wants them.

Hint 1:

"Mate in two or three" refers to two different sequences of moves, one leading to checkmate in two moves, the other to checkmate in three moves.

Hint 2:

The sequences of moves are helpmates, meaning black and white work together to make the checkmate possible.

Hint 3:

In the "mate in two" sequence, white gets checkmated in two moves. In the "mate in three" sequence, black gets checkmated in three moves.

Hint 4:

The "mate in two" sequence encodes the answer to the first question. The "mate in three" sequence encodes the answer to the second question.

Answer 1

An idea I had that may or may not be going anywhere:

The sayings look like those you spell out on a calculator.
If you draw the first one, you get:
Upside-down, it seems that it looks like various letters and numbers:
h85a06a4 (The 0 is the odd one out since all the rest are used to refer to squares.)
I doubt this is the exact method, but it seems promising.

Answer 2

White cannot force a checkmate in two or three moves. This is a help-mate puzzle, where White and Black work together to arrive a checkmate (this is hinted in the description of the chess puzzle: helpful clue, help you answer, hope it helps).

Even with Black's help, White cannot mate in two. However, White can help Black to mate in two: the unique sequence (found by f'') is

1. Rh2      Rf8
2. Rd2      Rf1#

There is also a (nearly) unique sequence for White to help-mate Black in three moves (which f'' also found):

1. c4         Kf7 (or Kf8)
2. O-O+    Ke7 (or Ke7 or Ke8)
3. Rae1#

There are two partial answers to the questions about grandpa, as well as two mating sequence, and the number of letters in the partial answers is the same as the number of letters in the mating sequences¹:

he gOeS By $\leftrightarrow$ RhRfRdRf (eight letters)

A smALL RIce $\leftrightarrow$ cKfOOKeRae (10 letters)

The partial answers have peculiar capitalization. Looking at the letters from the mating sequences corresponding to capitals in the partial answers yields:

he gOeS By ... fdR

A smALL RIce ... cOOKeR

So grandpa Herb's favorite president is Franklin Delano Roosevelt (who is often referred to by his initials, FDR), and on March 26, 1987, grandpa Herb bought a small rice cooker at the store.

1: The notation for castling in PGN format uses the letter 'O', while the FIDE handbook uses the numeral '0'. The difference is unfortunate, as the solution to this puzzle requires using the letter rather than the numeral.

Answer 3

The 2- and 3- move mates, for reference:

Black mating in 2 moves: 1. Rh2 Rf8 2. Rd2 Rf1#
White mating in 3 moves: 1. c4 Kf[7-8] 2. 0-0+ Ke[6-8] 3. Rae1#
According to OP, the possibilities for the king's moves in this sequence are not a problem.