fvqr

Rnpu zbivr vf pbaarpgrq gb gur bar rvgure fvqr bs vg ol na npgbe jub fgneerq va obgu.

Gurer unf gb or n fznyyrfg fdhner F3 nzbat gurz jvgu fvqr yratgu < 0.5*0.25 = cbjre(0.5,3).

Ner obgu urnegf ba rvgure fvqr bs gur oynax cbvagvat va gur fnzr qverpgvba (abegu fbhgu rnfg jrfg hc qbja)?

Vaivfvoyr jnyy haqre gur ebyyre pbnfgre, tvirf n cvcryvar geubhtu bevtva gb gur bgure fvqr.

Gur fznyyrfg fdhner nzbat gurz unf n fvqr yratgu < 0.5, yrg'f pnyy vg F1.

Vs ebcr 1 bayl ohearq bar dhnegre, gura vg jvyy gnxr gjragl-gjb naq n unys zvahgrf, abg svsgrra, nsgre yvtugvat gur bgure fvqr.

My informal counter proof by contradiction (decrypt with rot13.com): fvapr gur cnegvgvba vf svavgr, gurer vf n fdhner Z jvgu gur fubegrfg fvqr.

Abj pbafvqre gur fdhnerf nybat gur gbc fvqr bs gur havg fdhner.

Sybbe vg gb gur bgure fvqr naq lbh trg rfpncr irybpvgl.

Abj pbafvqre ebj bs fdhnerf pbirevat gur obggbz fvqr bs F1.

Naq fb ba - gurer vf nyjnlf n arkg ebj bs fdhnerf, nf gur fznyyrf fdhner va gur ebj pna abg gbhpu gur obggbz fvqr bs gur havg fdhner.

Obbx 4 jnf bar bs zl snibevgrf, vg pbzcyrgryl chgf gur znva fgbel gb gur fvqr naq tbrf onpx gb jura gur thafyvatre jnf nebhaq 14 ba bar bs uvf svefg zvffvbaf.