<span>along with units digit being < tens digit....let see if we can come up with something. ones unit must be 0,2,4,6,or 8. if 0 then tens unit can be 1-9 case1 if 2 then tens unit can be 3-9 case2 if 4 then tens unit can be 5-9 case3 if 6 then tens unit can be 7-9 case4 if 8 then tens unit can be 9 case5 : 108 is covered in case1 because 0<8 :</span><span>case5: 98----9+8=17 to be divisible by 9 hunderds unit has to be 1 and 198 is not divisible by 12 : case4:96,86,76...96---9+6=16 to be div by 9 100's unit has to be 3 and that is more than 200. 86 ...8+6=14 to be div by 9 100's unit has to be 4....to big same problem with 76 : case3:94,84,74,64,54...9+4, 8+4,7+4,6+4,5+4 all present problems with #'s larger than 200 : case2:92,82,72,62,52,42,32 ...92,82,and 72 all get throw out because #'s larger than 200. 62 is 6+2=8..to be divisble by 9 100's unit must be 1...162..not divisible by 12 take 52,42,32 end up with being over 200 : case1:90,80,70,60,50,40,30,20,10... 90 larger than 200...80 is 8+0=8 in order to be divisible by 9 100's unit has to be 1. 180.......guess what this number is divisible by 9 and 12 and is less than 200 applying divisibility rules for the rest of the numbers in this case make all the numbers to large >200 : SO WE HAVE GONE THROUGH ALL THE CASES AND 180 is the only one that qualified there could be a simpler way but I will have to think on that</span>lets work backwards
