The word unsolvability is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.
Words With Friends™ Letter Score: 26
Highest Scoring Words With Friends™ Play In The Letters unsolvability
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Seven Letter Word Alert: (46 words)
ability, abvolts, albinos, bailout, ballots, bastion, billion, biotins, bluntly, bolivia, botulin, bullion, buoyant, butanol, install, instill, layouts, liaison, lousily, lovably, lustily, nastily, noisily, notably, nullity, obtains, outlays, outsail, saintly, saltily, solubly, stonily, stylion, suavity, sunlily, synovia, tonally, tunably, unbaits, unbolts, unsilty, villain, violins, violist, visibly, vitally