Working backwards an excellent 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?
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 meeting the 3rd watchman he had =8
Before meeting the 2nd watchman he had = 20
Before meeting the 1st watchman he had = 44
The thief stole 44 diamonds.