Mathematical Recreations

Whilst reminiscing what I did 60 years back (I am 81 now), in my spare time when I was alone by myself and when there was no TV, mobile phone, computer, Internet or even a ball point pen I found that I amused myself with Mathematical recreations, reading such books and using a Venus 1B Pencil to make notes or solve a problem. Of course when I had friends or family we played Cricket Tennis etc and when indoors, Draughts, Monopoly, Cards, etc. Even today I am intrigued by the subject though I find it more difficult or impossible to solve many problems that I used to earlier. One such Arithmetical Recreation was the FOUR FOURS PROBLEM. I had solved the problem and had written in my book which I was intending publishing one day. Now when I googled “Four Fours” on my computer I was surprised to find many solutions (some wrong and inelegant). And even Wikipedia covered the problem. Nevertheless I wished to blog my solution.

THE FOUR FOURS PROBLEM

The objective of the four fours problem is to find a mathematical expression for every integer from 1 to 100; using only common mathematical symbols and exactly four fours (no other digits are allowed). The rider I add is to express these in the simplest possible manner.

Operations and symbols that are allowed include the four arithmetic operations (+, ×, -, /), concatenation (e.g. the use of 44), decimal points (e.g. 4.4), powers (e.g. 44), square roots, factorials (4! - which is 4 x 3 x2 x 1 =24), and overbars for repeating decimal (e.g. .4 with an over bar to express 0.44444….) – I found that to express 6 numbers I had to resort to this.)