World's 200 Hardest Brain Teasers (13 page)

Also,
BCD =
BDC = 50° so BD = BC = BG, and triangle BDG is equilateral.

But
GBE = 40° =
BEG, so BG = GE = GD.

And
DGE = 40°. Since DG = EG,
GDE =
DEG = 70° and since
BEG = 40°,
BED = 30°.

139. (c) 2/3

Probability can be defined as the favorable number of possible outcomes divided by the total number of possible outcomes. Since one of the coins lands as a head, the total number of ways this is possible is the following:

five-cent head, ten-cent tail

five-cent head, ten-cent head

five-cent tail, ten-cent head

There couldn’t be a possibility of a ten-cent tail, ten-cent tail combination because we are told that one of the coins must be a head.

So there are three possibilities.

Now, the favorable ways that the five-cent coin will land as a head are:

five-cent head, ten-cent tail

five-cent head, ten-cent head

That is two ways out of three possible ways. Thus, the probability is 2/3.

140. (b) The equivalent discount of each of the three items is between 70 percent and 80 percent.

Suppose we start with a price of $100 for each item. After the first discount, the first item will be $40. After the second discount, the item will be $24. This would represent an equivalent discount of 76 percent. Use the same process for the second and third item. For the second item, we would find that the price after the second discount is $25, which would represent an equivalent discount of 75 percent. For the third item, we would find the equivalent discount to be 79 percent. Thus, (b) is correct.

141. Fill the three-gallon bottle with milk, then pour the three gallons of milk into the five-gallon bottle. Now again fill the three-gallon bottle with milk and pour milk from the three-gallon bottle into the five-gallon bottle until you fill it. You have one gallon left in the three-gallon bottle.

142. FIVE TWO FIVE; TWO FIVE TWO

Spade Spade Club; Spade Spade Club

143. (c) The number of false statements here is three.

If there are three false statements, then C is true and A, B, D, are false.

144. 1,349

Represent the digits as
a, b, c, d.
So (1)
a
= (1/3)
b
, (2)
c
=
a
+
b,
and (3)
d
= 3
b
.

From (1) we get (4) 3
a
=
b
. From (3) and (4) we get (5)
d
= 9
a
. The only way (5) can be true is if
a
= 1, since
d
is a single digit and not equal to 0, making
d
= 9. Thus, from (1)
b
= 3, and from (2)
c
= 4. So the number
abcd
is 1,349.

145. They are both lying.

Scenario 1: If the child with brown hair is lying, he is a boy. Then the child with blond hair must be a girl since there is a boy and a girl and thus is also lying.

Scenario 2: If the child with brown hair is not lying, then she’s a girl. Since at least one of them is lying, the child with blond hair must be lying and would be a girl also, which is impossible. So the only possibility is the first scenario where both are lying.

146. Method 1: First weigh six balls with six balls. Whichever of the six balls tips the scale, that is where the heavier ball is. So now from those balls, weigh three against three. Again whichever of the three tips the scale is where the heavier ball is. So of the three balls (where one of them is heavier than the other two) weigh one against one. If they balance, the heavier ball is the remaining one. If they don’t balance, whichever ball tips the scale is the heavier one.

Method 2: First weigh four balls with four balls. Suppose they balance. Then weigh the remaining four balls—two balls against two balls. Whichever two balls tip the scale downward include the heavier ball. So weigh one of those balls against the other. Whichever ball tips the scale downward is the heavier ball.

Suppose when we weigh the four balls against four balls, they don’t balance. The four balls that tip the scale downward have one of the balls that is heavier. So take these four balls and weigh two against two. One of the two balls will tip the scale downward. Whichever of the two balls tips the scale downward contains the heavy ball. Now weigh one of those balls with the other. The one that tips the scale downward is the heavy ball.

Method 3: First weigh three against three. If they balance, then weigh the other three against three. Certainly one side will be heavier so weigh the three balls where one is heavier, one against one. If they balance, it’s the remaining ball that is heavier. If they don’t balance, the ball that tips the scale downward is heavier.