1. Replace the number signs with mathematical symbols to make this equation work:

7 # 7 # 77 # 7 # 7 = 497

7 + 77 * 7 - 7 * 7 = 497.

2. Insert one ÷ to make the result of this sequence of numbers: 135916308, be equal to 1 ÷ 12

3. Two years ago, a man offered to sell his Chevy to a car dealership for $7000,but they declined to buy it. A year later the seller offered the same car
for $6000, but again the car dealer decided not to purchase it. A few months later the man offered the Chevy for $5142.85, but yet again the car
dealership refused to buy it. Yesterday, the car was offered for $4,408.16. The car dealer still did not want to purchase the car. If
the owner offers the car for sale again, and he maintains a consistent reduction, how much will the offer be?

The car will be offered for $3778.42. The car was reduced by 6/7 of its price each time. The numbers are rounded off; so your answer may vary by a few cents.

4. A chessboard has squares that are two inches by two inches. What is the
diameter of the largest circle that can be drawn on the board in such a way that the circle's circumference is entirely on black squares?

The diameter is 6.824 inches. If you place the point of a compass at the center of a black square on a chessboard with two inch squares, and extend the arms of the compass a distance equal to the square root of 10 inches which is 3.162 inches, the pencil will trace the largest possible circle that touches only black squares. The diameter is, of course, equal to twice the radius.

5. What is the number which is 4 more than the number that is double one-fifth of one-tenth of 900?

40. 900 ÷ 10 = 90 ÷ 5 = 18 X 2 = 36 + 4 = 40.

6. Using any or all of the mathematical symbols +, -, x and/or parentheses between the digits to make 579.

1 2 3 4 5 6 = 579

1 2 3 + 4 5 6 = 579. This is one solution, you may have found others.

7. Sue is now four-fifths of her sister Kate's age. Three
years ago, she was one-half her sister's age. Five years from now, Sue will be nine-tenths of Kate's age. If they are both under age 10, how old
are they now?

8. If 1/3 of some number is 1/17 of 1/5, what is that number?

3/85. 1/3x = 1/17 x 1/5 1/3x = 1/85 x = 3/85.

9. What is the 4-digit number (no zeros) in which the first and last digits are the
same, the second digit is half the sum of the second and the fourth, and the last digit is half the sum of the first and third? (the sum of all
digits is 24)

10. The beach resort held a contest to guess the number of beach balls in the net
bag. Alice guessed 20, Bill guessed 21, Charlie guessed 22, Dick guessed 17 and Ed guessed 16. One was off by 4, one was off by 3, one by 1, one by
2 and one was correct. How many beach balls were there?