## 51. The owner of a local jewellery store hired 3 watchmen 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 $$\frac{1}{2}$$ of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?

## 52. The number of employees in Examveda and Co. is a prime number and less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

## 53. The remainder , when (2222^{5555} + 5555^{2222}) is divided by 7, is

^{5555}+ 5555

^{2222}) is divided by 7, is

## 54. A young girl counted in the following way on the fingers of her left hand. She started calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index finger 8, thumb 9 and then back to the index finger for 10, middle finger for 11 and so on. She counted up 1994. She ended on her

## 55. How many pairs of natural numbers is there the difference of whose squares are 45.

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