Working backwards an excelleng problem solving approach The owner of a jewellery shop hired three watchman to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman,one at a time. to each he gave ½ of the diamonds he had then, and 2 more besides. He escaped with two diamonds. How many did he steal originally? Analysis Make a diagrammatic plan of diamond distribution. Also notice, that the thief left with only 2 diamonds. Let x be the number of diamonds he was left with i.e. 2. Before the thief met the third watchman he would have had double the number of diamonds and 2 extra diamonds. Hence if x is the diamonds the thief is left with, before meeting the watchman he would be left with 2x+2 = (x+2)2 diamonds Thief escaped with 2 diamonds. Before 3rd watchman he had =8 Before 2nd watchman he had = 20 Before 1st watchman he had = 44 The thief stole 44 diamonds. Working backwards is an excellent problem solving strategy. 
