There are two parts to this regular feature: Normal and Abnormal. Normal is open to all school students, while Abnormal is open to everyone, teachers included. Send us your answers with working. The best entries will be mentioned in the next issue. Prizes are $75 and $50 for the Normal section and $100 and $75 for the Abnormal, and are again kindly partially sponsored by Mr & Mrs Farai Nyabadza. You are encouraged to send in your solutions even if you cannot answer all questions. The deadline is 31st May 2000.
(Please send in your solutions to different questions on different sheets of paper, with name and address on each.)
Normal Section
1. The salary of the first worker is 25 percent greater than the salary of the second one. How much less (in percentage) is the salary of the second worker than the salary of the first one ?
2. If a certain two-digit number is divided by the product of its digits then the quotient is 1 and remainder is 16. If the product of its digits is added to the square of the difference of the digits then the original number is obtained. Find this number. Solve the problem if only the first condition is given.
3. abc = 1, a+b+c = 1/a+1/b+1/c. Prove that at least one of a, b or c equals 1.
Abnormal Section
1. There is a number 458 on the blackboard. During one step one may replace a digit with a double one or one may erase the last digit. How many steps to get the number 14?
2. Find the real solutions of the following system
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3. Each of the natural numbers a, b, c, and d is a multiple of ab-cd (also positive). Show that ab-cd = 1.