Unless otherwise noted, all these deck construction challenges allow alpha/beta lands as usual.
Get Equipped!: Your deck must consist entirely of equipment cards. You start three 0/1 kobolds in play (or something similar.) Alternatively, it could allow six cards that break the rule, but something about starting with a few 0/1 creatures seems more interesting.
Auramancy: Every card in your deck must be an aura. You may have six cards that break this rule.
Power of One: Every card in your deck must have a CMC of exactly one.
Mirrored Colors: Your deck cannot have any mana sources (even the beta lands are banned), nor any artifacts or colorless cards -- with the exceptions of
Exotic Orchard,
Fellwar Stone,
Quirion Explorer,
Sylvok Explorer, and
Benthic Explorers (that is, mana sources that can only produce colors of mana your opponent can produce.) You may have any number of copies of
Exotic Orchard in your deck.
(Alternative to the above:)
Mad Lands: At the start of each duel, the game chooses from 1-5 colors at random, then replaces all lands in your deck with random basic lands of those colors. You may not use any artifacts or colorless cards.
Unrestricted: You may ignore all limits on deck construction, save that you must have at least 60 cards. Your opponent starts with 60 life and a
Chromatic Lantern in play, and draws an extra card each turn. (Probably your opponent needs more of an advantage for this to be fair.)
Balanced Out: Your deck must have an equal number of mono-color cards of each color. No gold cards are allowed, and aside from alpha/beta lands, no colorless cards, either.
Paralyzed: Skip your untap phase. (This might be too harsh to be winnable; so perhaps allow them to untap one basic land per turn, or even just allow their basic lands to untap normally? On the other hand, it's fun to think of ways to beat it when you get no untap phase at all and no compensation.)
Fading...: Every card in your deck must have Fading, Cumulative Upkeep, Phasing, or Echo.
Junkyard: Excluding beta lands, your entire starting hand and all cards you draw from your deck are immediately discarded.
Repetition: Each round, half the cards in your deck are replaced by copies of one particular card. (Eg. half your deck is replaced by Goblin Welders one round; Clones another, etc etc etc.)