Code to solve 4 4's problem : write each of the numbers 1 to 100 using exactly four 4's for each number
![[Graphics:Images/FourFours_gr_1.gif]](Images/FourFours_gr_1.gif)
![[Graphics:Images/FourFours_gr_2.gif]](Images/FourFours_gr_2.gif)
![[Graphics:Images/FourFours_gr_3.gif]](Images/FourFours_gr_3.gif)
now for each function,make a function that performs on the first element, and keeps a record in the 2nd
![[Graphics:Images/FourFours_gr_4.gif]](Images/FourFours_gr_4.gif)
![[Graphics:Images/FourFours_gr_5.gif]](Images/FourFours_gr_5.gif)
![[Graphics:Images/FourFours_gr_6.gif]](Images/FourFours_gr_6.gif)
![[Graphics:Images/FourFours_gr_7.gif]](Images/FourFours_gr_7.gif)
![[Graphics:Images/FourFours_gr_8.gif]](Images/FourFours_gr_8.gif)
![[Graphics:Images/FourFours_gr_9.gif]](Images/FourFours_gr_9.gif)
![[Graphics:Images/FourFours_gr_10.gif]](Images/FourFours_gr_10.gif)
![[Graphics:Images/FourFours_gr_11.gif]](Images/FourFours_gr_11.gif)
![[Graphics:Images/FourFours_gr_12.gif]](Images/FourFours_gr_12.gif)
![[Graphics:Images/FourFours_gr_13.gif]](Images/FourFours_gr_13.gif)
![[Graphics:Images/FourFours_gr_14.gif]](Images/FourFours_gr_14.gif)
![[Graphics:Images/FourFours_gr_15.gif]](Images/FourFours_gr_15.gif)
![[Graphics:Images/FourFours_gr_16.gif]](Images/FourFours_gr_16.gif)
![[Graphics:Images/FourFours_gr_17.gif]](Images/FourFours_gr_17.gif)
![[Graphics:Images/FourFours_gr_18.gif]](Images/FourFours_gr_18.gif)
![[Graphics:Images/FourFours_gr_19.gif]](Images/FourFours_gr_19.gif)
![[Graphics:Images/FourFours_gr_20.gif]](Images/FourFours_gr_20.gif)
![[Graphics:Images/FourFours_gr_21.gif]](Images/FourFours_gr_21.gif)
![[Graphics:Images/FourFours_gr_22.gif]](Images/FourFours_gr_22.gif)
![[Graphics:Images/FourFours_gr_23.gif]](Images/FourFours_gr_23.gif)
![[Graphics:Images/FourFours_gr_24.gif]](Images/FourFours_gr_24.gif)
![[Graphics:Images/FourFours_gr_25.gif]](Images/FourFours_gr_25.gif)
![[Graphics:Images/FourFours_gr_26.gif]](Images/FourFours_gr_26.gif)
![[Graphics:Images/FourFours_gr_27.gif]](Images/FourFours_gr_27.gif)
![[Graphics:Images/FourFours_gr_28.gif]](Images/FourFours_gr_28.gif)
![[Graphics:Images/FourFours_gr_29.gif]](Images/FourFours_gr_29.gif)
![[Graphics:Images/FourFours_gr_30.gif]](Images/FourFours_gr_30.gif)
![[Graphics:Images/FourFours_gr_31.gif]](Images/FourFours_gr_31.gif)
Now we start making lists of numebrs, starting with numbers reachable from one 4: 4, .4 = 4/10, and .4 repeating = 4/9, and we apply all unary ops to them
![[Graphics:Images/FourFours_gr_32.gif]](Images/FourFours_gr_32.gif)
![[Graphics:Images/FourFours_gr_33.gif]](Images/FourFours_gr_33.gif)
![[Graphics:Images/FourFours_gr_34.gif]](Images/FourFours_gr_34.gif)
![[Graphics:Images/FourFours_gr_35.gif]](Images/FourFours_gr_35.gif)
![[Graphics:Images/FourFours_gr_36.gif]](Images/FourFours_gr_36.gif)
![[Graphics:Images/FourFours_gr_37.gif]](Images/FourFours_gr_37.gif)
![[Graphics:Images/FourFours_gr_38.gif]](Images/FourFours_gr_38.gif)
![[Graphics:Images/FourFours_gr_39.gif]](Images/FourFours_gr_39.gif)
![[Graphics:Images/FourFours_gr_40.gif]](Images/FourFours_gr_40.gif)
![[Graphics:Images/FourFours_gr_41.gif]](Images/FourFours_gr_41.gif)
![[Graphics:Images/FourFours_gr_42.gif]](Images/FourFours_gr_42.gif)
![[Graphics:Images/FourFours_gr_43.gif]](Images/FourFours_gr_43.gif)
![[Graphics:Images/FourFours_gr_44.gif]](Images/FourFours_gr_44.gif)
![[Graphics:Images/FourFours_gr_45.gif]](Images/FourFours_gr_45.gif)
![[Graphics:Images/FourFours_gr_46.gif]](Images/FourFours_gr_46.gif)
![[Graphics:Images/FourFours_gr_47.gif]](Images/FourFours_gr_47.gif)
![[Graphics:Images/FourFours_gr_48.gif]](Images/FourFours_gr_48.gif)
![[Graphics:Images/FourFours_gr_49.gif]](Images/FourFours_gr_49.gif)
![[Graphics:Images/FourFours_gr_50.gif]](Images/FourFours_gr_50.gif)
![[Graphics:Images/FourFours_gr_51.gif]](Images/FourFours_gr_51.gif)
![[Graphics:Images/FourFours_gr_52.gif]](Images/FourFours_gr_52.gif)
![[Graphics:Images/FourFours_gr_53.gif]](Images/FourFours_gr_53.gif)
![[Graphics:Images/FourFours_gr_54.gif]](Images/FourFours_gr_54.gif)
![[Graphics:Images/FourFours_gr_55.gif]](Images/FourFours_gr_55.gif)
![[Graphics:Images/FourFours_gr_56.gif]](Images/FourFours_gr_56.gif)
![[Graphics:Images/FourFours_gr_57.gif]](Images/FourFours_gr_57.gif)
![[Graphics:Images/FourFours_gr_58.gif]](Images/FourFours_gr_58.gif)
![[Graphics:Images/FourFours_gr_59.gif]](Images/FourFours_gr_59.gif)
![[Graphics:Images/FourFours_gr_60.gif]](Images/FourFours_gr_60.gif)
![[Graphics:Images/FourFours_gr_61.gif]](Images/FourFours_gr_61.gif)
Solutions for the first 150 integers....
![[Graphics:Images/FourFours_gr_62.gif]](Images/FourFours_gr_62.gif)
![[Graphics:Images/FourFours_gr_63.gif]](Images/FourFours_gr_63.gif)
Converted by Mathematica
November 5, 2001