# Math Puzzle 9

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1) It is the end of financial year. Alley has to pay 8% interest on $500 she borrowed from Sam. In turn Sam has to pay 12% interest on $350 he took from his cousin Tommy. But Tommy himself took $940 on loan from Alley at an interest of 5%. Will anyone of them make a profit this year?

2) Alley’s grandfather is a bit older than her grandmother. In fact the difference between the squares of their ages is exactly 1988. How old are they?

3) Alley and Sam each have a square picture of their favourite animal hanging above their beds-a hippopotamus for Sam and a seal for Alley. Each photograph is an exact whole number of centimeters along a side but Sam’s is slightly bigger than Alley’s. When they add up the areas of their photos they found that the answer is 1985〖cm]

^{2}. What are the sizes of two pictures?

4) Alley and Sam have invited three friends to have coffee. They have two jugs : one contains milk and the other four times as much coffee. They also have five cups , all of the same size, and they pour milk and coffee, according to each individual’s wishes. Sam takes black coffee, Alley takes half milk and half coffee, and three friends each like one quarter milk and the rest coffee. By filling the cups in this manner, one of the is emptied exactly. Which one? How much is left in the other?

5) Sam and his cousin Tommy just celebrated their birthdays on the same day. Tommy is now four times as old as Sam is now. Sam is a teenager. How old are the two boys?

6) Alley has just bought a combination lock for the chest in which she keeps her diary. She has to select three numbers forming a Pythagorean triplet for the combination. She can choose the following:

2, 7, 8, 9, 11, 12, 15, 16, 17, 20, 22, 23, 24, 25, 30, 34, 41, 56. Which are her options?

7) On a particular game, the score for the second roll is five more than the score for the first; the score for the third roll is six less than that of the second; the score for the fourth roll is eleven more than that of the third; and the score for the fifth roll is eight less than that of the fourth. What was the score for each of these five throws?

8) A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

9) You must cut a birthday cake into exactly eight pieces, but you're only allowed to make three straight cuts, and you can't move pieces of the cake as you cut. How can you do it?(math puzzle 9)

10) You want to hire a temporary employee for one month. You offer him reasonable wages, but the employee suggests an alternative. For the first day of work, he will be paid a penny. For the second day, two pennies. For the third day, four pennies. The salary for each subsequent day will be double the previous day's, until the one month term is over. Ignoring the legalities of such a situation, would it be a good idea to accept the potential employee's proposal?

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