In order to do many of the operations and processes in mathematics, we need to follow certain rules.   There are rules for addition, subtraction, multiplication, division, decimals, solving equations, proving trig identities, etc.

Lewis Carroll came up with the idea of word ladders.
There is only one RULE for Word Ladders:
Change ONLY one letter at a time and form a new word at each step.
For instance, you might go from COAT to SHOE as follows:
COAT, COOT, SOOT, SHOT, SHOE.

#1 Change LAST to WORD

#2 Change SHOW to CASE

Solution to the Problem:
Alternate solutions with the name of the first person to send them in are also listed.

#1 Change LAST to WORD
        LAST, LOST, LOSE, LORE, LORD, WORD
        LAST, LOST, LOSE, LORE, WORE, WORD (John Funk)
        Last, Past, Part, Wart, Wort, Word (Jeremy Harmon)
        LAST, FAST, FART, FORT, FORD, WORD (Jacob Harmon)
        Last, Cast, Cart, Card, Cord, Word (Michael Black)
        LAST-lost-loot-toot-tool-wool-wood-WORD (Wynston Anglen)

#2 Change SHOW to CASE
        SHOW, SHOT, SOOT, COOT, COST, CAST, CASE
        SHOW, SHOT, SLOT, SLAT, FLAT, FEAT, FEST, FAST, CAST, CASE (John Funk)
        Show, Slow, Plow, Plot, Clot, Coot, Cost, Cast, Case (Steve Muller)
        Show, Slow, Blow, Blot, Clot, Coot, Cost, Cast, Case (Austin Hale)
        show, slow, glow, grow, crow, crot, coot, cost, cast, case (Hazen Dickerson)
        SHOW-shot-soot-loot-lost-last-cast-CASE (Wynston Anglen)