Knuth's conjecture writing integers "using only one 4"

[Jonathan Post]

For an update and a related problem, see:
http://magicdragon.com/math.html
then scroll and/or click to these sections:
Four Nines Puzzle
"The Weekly Dispatch" of 4 February 1900, which ran a puzzle column by Dudeney,introduced a problem which is still provoking interest today.  That problemwas the Four Nines Puzzle, based on the even older Four Fours Puzzle, which isalso discussed on this web page. Jonathan's page hotlinked here includes acomplete list of equations representing, with four nines, every integer upto 314, and many beyond that.  There is some deep theory towards the bottomof the page.
Four π Puzzle
Similar to the Four Nines Puzzle, and Four Fours Puzzle, mentioned above,What numbers can be made with four copies of the number "pi", or π?Jonathan's page hotlinked here includes a complete list of equationsrepresenting,with four "pi", every integer up to 1,000, and many beyond that.
It is a useful teaching tool for geometry oralgebra students to ask: "How can we construct the smaller whole numbers,under 100 for instance, using only all four copies of the number π,parentheses, and the arithmetic operators"+","-","x","/"?
We also allow the use of exponentiation, radicals(especially the square root "sqrt"), factorial "!", and the floor function"|_ N _|" and ceiling function "|- N -|".