Four Fours/Further Results

== Puzzle ==
Using exactly $4$ instances of the number $4$, it is possible to write an expression for all positive integers from $0$ to $100$, using whatever arithmetical operations are necessary.
It is also possible to populate the table for numbers from $101$ to $200$, although for $197$ we appear to need to use the floor function.
== Solution ==
==== Four Fours: $101$ ====
==== Four Fours: $102$ ====
==== Four Fours: $103$ ====
==== Four Fours: $104$ ====
==== Four Fours: $105$ ====
==== Four Fours: $106$ ====
==== Four Fours: $107$ ====
==== Four Fours: $108$ ====
==== Four Fours: $109$ ====
==== Four Fours: $110$ ====
==== Four Fours: $111$ ====
==== Four Fours: $112$ ====
==== Four Fours: $113$ ====
==== Four Fours: $114$ ====
==== Four Fours: $115$ ====
==== Four Fours: $116$ ====
==== Four Fours: $117$ ====
==== Four Fours: $118$ ====
==== Four Fours: $119$ ====
==== Four Fours: $120$ ====
==== Four Fours: $121$ ====
==== Four Fours: $122$ ====
==== Four Fours: $123$ ====
==== Four Fours: $124$ ====
==== Four Fours: $125$ ====
==== Four Fours: $126$ ====
==== Four Fours: $127$ ====
==== Four Fours: $128$ ====
==== Four Fours: $129$ ====
==== Four Fours: $130$ ====
==== Four Fours: $131$ ====
==== Four Fours: $132$ ====
==== Four Fours: $133$ ====
==== Four Fours: $134$ ====
==== Four Fours: $135$ ====
==== Four Fours: $136$ ====
==== Four Fours: $137$ ====
==== Four Fours: $138$ ====
==== Four Fours: $139$ ====
==== Four Fours: $140$ ====
==== Four Fours: $141$ ====
==== Four Fours: $142$ ====
==== Four Fours: $143$ ====
==== Four Fours: $144$ ====
==== Four Fours: $145$ ====
==== Four Fours: $146$ ====
==== Four Fours: $147$ ====
==== Four Fours: $148$ ====
==== Four Fours: $149$ ====
==== Four Fours: $150$ ====
==== Four Fours: $151$ ====
==== Four Fours: $152$ ====
==== Four Fours: $153$ ====
==== Four Fours: $154$ ====
==== Four Fours: $155$ ====
==== Four Fours: $156$ ====
==== Four Fours: $157$ ====
==== Four Fours: $158$ ====
==== Four Fours: $159$ ====
==== Four Fours: $160$ ====
==== Four Fours: $161$ ====
==== Four Fours: $162$ ====
==== Four Fours: $163$ ====
==== Four Fours: $164$ ====
==== Four Fours: $165$ ====
==== Four Fours: $166$ ====
==== Four Fours: $167$ ====
==== Four Fours: $168$ ====
==== Four Fours: $169$ ====
==== Four Fours: $170$ ====
==== Four Fours: $171$ ====
==== Four Fours: $172$ ====
==== Four Fours: $173$ ====
==== Four Fours: $174$ ====
==== Four Fours: $175$ ====
==== Four Fours: $176$ ====
==== Four Fours: $177$ ====
==== Four Fours: $178$ ====
==== Four Fours: $179$ ====
==== Four Fours: $180$ ====
==== Four Fours: $181$ ====
==== Four Fours: $182$ ====
==== Four Fours: $183$ ====
==== Four Fours: $184$ ====
==== Four Fours: $185$ ====
==== Four Fours: $186$ ====
==== Four Fours: $187$ ====
==== Four Fours: $188$ ====
==== Four Fours: $189$ ====
==== Four Fours: $190$ ====
==== Four Fours: $191$ ====
==== Four Fours: $192$ ====
==== Four Fours: $193$ ====
==== Four Fours: $194$ ====
==== Four Fours: $195$ ====
==== Four Fours: $196$ ====
==== Four Fours: $197$ ====
==== Four Fours: $198$ ====
==== Four Fours: $199$ ====
==== Four Fours: $200$ ====
== Glossary ==
Category:Four Fours