Would any kind soul with a Merck index handy look up the solubility of KOH in EtOH/IsOH/MeOH?  I would be greatly in your debt.

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over and under, then back to the start
this sidewalk's bottom is the same as its top

Monograph number: 7806
Title: Potassium Hydroxide. 
CAS Registry number: [1310-58-3]
Additional name(s): Potassium hydrate; caustic potash; potassa. 
Molecular formula: HKO
Molecular weight: 56.11
Composition: H 1.80%, K 69.69%, O 28.52%. 
Line formula: KOH. 
Literature references: Prepd industrially by electrolysis of potassium chloride:  Faith, Keyes Clark's Industrial Chemicals, F. A. Lowenheim, M. K. Moran, Eds. (Wiley-Interscience, New York, 4th ed., 1975) pp 674-678. Toxicity:  H. F. Smyth et al., Am. Ind. Hyg. Assoc. J. 30, 470 (1969).
Properties: White or slightly yellow lumps, rods, pellets. Very caustic to tissue.  Rapidly absorbs moisture and CO2 from the air and deliquesces. mp about 360 deg; mp 380 deg when anhydr.  Sol in 0.9 part water, about 0.6 part boiling water, 3 parts alcohol, 2.5 parts glycerol. When dissolved in water or alcohol or when the soln is treated with an acid, much heat is generated.  Keep tightly closed and do not handle with bare hands.  A 0.1M aq soln has a pH of 13.5.  LD50 orally in rats:  1.23 g/kg (Smyth).
Melting point: 360; 380
Caution:  Extremely corrosive.  Ingestion may produce violent pain in throat and epigastrium, hematemesis, collapse.  If not immediately fatal, stricture of esophagus may develop, cf. Clinical Toxicology of Commercial Products, R. E. Gosselin et al., Eds. (Williams Wilkins, Baltimore, 4th ed., 1976) Section III, pp 206-212.

USE:  Manuf liq soap; mordant for wood; absorbing CO2; mercerizing cotton; paint and varnish removers; electroplating,photoengraving and lithography; printing inks; in analytical chemistry and in organic syntheses.  Pharmaceutic aid (alkalizer).
THERAP CAT (VET):  Caustic.  In disbudding calves' horns.  In aq solution to dissolve scales and hair in skin scrapings. 

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I've got nothing to do today but smile !

in three parts of alcohol, excellent, thank you!

Damn, you got the electronic version, makin' me all jealous...

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over and under, then back to the start
this sidewalk's bottom is the same as its top

When they say alcohol, I think they are refering to ethanol, solubilties maybe different for other alcohols.

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I've got nothing to do today but smile !

Elementary: That's correct.

I think you can dissolve 15-20% of KOH in IPA, and at least twice that in methanol.