Brainteasers 2

1. How many years were there between Jan. 1, 5 B.C. and Jan. 1, 5 A.D.?

2. My daughter is twice as old as my son and half as old as I am. In twenty-two years my son will be half my age. How old is my daughter?

3. Here is a simple algebraic proof:

Given x = 1 and y = 1, then:
x = y
Multiplying each side by x,
we get
x2 = xy
Subtracting y2 from each side, we get:
x2 - y2 = xy - y2
Factoring each side,
we get:
(x + y) (x - y) = y (x - y)
Dividing by the common term
(x - y), we get:
x + y = y
Substituting the given values,
we get:
1 + 1 = 1
Therefore:
2 = 1.

What is the mistake?

4. If 6 boys fill 6 notebooks in 6 weeks, and 4 girls fill 4 notebooks in 4 weeks, how many notebooks will a class of 12 girls and 12 boys fill in 12 weeks?

5. "O" is the center of the circle. AB is parallel to OD. AO and BC are perpendicular to OD. OC is five light-years long, and CD is 1 light-year long. What is the length of AC?

6. Jack said to his sister, Jill, "Mary is my niece." "She is not my niece," said Jill. How is this possible?

7. A "Cross-number" Puzzle:

Across:
1. The cube of a whole number.
5. The number of square inches in a square yard.
6. The number of cubic inches in a cubic foot.
7. The number of millimeters in a meter.

Down:
1. A number which is unchanged if the digits are reversed.
2. A prime number.
3. The number of feet in a mile.
4. The number of seconds in an hour.

8. When you travel through the Panama Canal and go from the Atlantic Ocean to the Pacific Ocean, do you travel from east to west or from west to east?

9. How many squares are there in the figure below?

10. Here is an addition problem, with a subtotal, which a son sent to his father on his birthday. Each letter represents a different number. Find the numbers.
Just to be sure, it's clear:
You add HAPPY + BIRTH + DAY and the answer is DTATH Then you add DTATH + DADDY and the answer is ITXHI.

Answers.

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