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## Math tip 8 (Updated On Thursday, September 05, 2013) << Back to Page

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.

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