BARBIT

In 15 seconds, answer this question: If you rearrange the letters "BARBIT", you would have the name of a:

OCEAN - COUNTRY - STATE - CITY - ANIMAL



 

Answer:

ANIMAL "BARBIT" = RABBIT.

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

Ladders

In an alley two ladders are placed cross-wise. The lengths of these ladders are 2 and 3 meters. They cross one another at one meter above the ground. What is the width of the alley?

 

Answer:

Define the following variables (see the figure on the right):
x is the height at which the ladder of 2 meters touches the wall of the alley;
 y is the height at which the ladder of 3 meters touches the wall of the alley;
 a is the horizontal distance between the point where the ladders cross and the wall to which the ladder of 2 meters is standing;
 b is the horizontal distance between the point where the ladders cross and the wall to which the ladder of 3 meters is standing;
 w is the width of the alley (equals a+b);
 h is the height at which the ladders cross (1 meter).

Because of the similarity of triangles,
x / w = h / b
and
y / w = h / a
so
b = (w × h) / x
and
a = (w × h) / y.
Combining this with
a + b = w
gives
(w × h) / y+(w × h) / x = w
from which it follows that
h × x + h × y = x × y
from which we conclude that
y = (h × x) / (x - h).
Because of Pythagoras' theorem,
w = sqrt(32 - y2) = sqrt(9 - y2)
and
w = sqrt(22 - x2) = sqrt(4 - x2).
Combining these two equations gives
9 - y2 = 4 - x2
so
y2 - x2 = 5.
Combining this with
y = (h × x) / (x - h)
and h = 1, results in:
(x / (x - 1))2 - x2 = 5.
Solving this equation gives:
x = 1/2 + (sqrt(c) + sqrt((24 × sqrt(2) / sqrt(c)) - c -14)) / (2 × sqrt(2))
where
c = 2 × (d + (25 / d) - 7) / 3
and
d = (395 + 60 × sqrt(39))1/3.
And since w = sqrt(4 - x2), this gives 1.231185724... meters for the width of the alley.

It is interesting to note that there are combinations of integer ladder lengths and an integer crossing height, for which the width of the alley is also an integer value. The combination with the smallest values for which this is the case, is the following one:
 shortest ladder: 70,
 longest ladder: 119,
 crossing height: 30,
 width of the alley: 56.

Antique Car Auction

A man is going to an Antique Car auction. All purchases must be paid for in cash. He goes to the bank and draws out $25,000.

Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15. Each envelope contains the least number of bills possible of any available US currency (for example, no two tens instead of a twenty).

At the auction he makes a successful bid of $8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount.

How many ones did the auctioneer find in the envelopes?

 

Answer:

One.
Unfortunately, Lucas Jones didn't provide a more elaborate explanation. But thanks to Ronald A. Laski we can now present a more acceptable explanation:

In Envelope #14, there are:
    81 $100 bills = $8100
     1 $ 50 bill  = $  50
     2 $ 20 bills = $  40
     1 $  2 bill  = $   2
                    ----- +
                    $8192 (total amount of money for Envelope #14) In Envelope #8, there are:      1 $100 bill  = $100
     1 $ 20 bill  = $ 20
     1 $  5 bill  = $  5
     1 $  2 bill  = $  2
     1 $  1 bill  = $  1 <- that's the one!
                    ----
                    $128 (total amount of money for Envelope #8)

Envelope #2 has 1 $2 bill in it, which is its total amount also.
Now $8192 + $128 + $2 = $8322. And that is the winning bid!
The amount of money in each envelope is 2 ^ (# of envelope - 1), except for envelope 15, which contains $8617.

Net-19

This net has nineteen circles that have to be filled with the numbers 1 up to 19. These numbers have to be placed in such a way that all numbers on any horizontal row and any diagonal line add up to the same sum. How should the nineteen numbers be placed in the net?

 

Answer:

As you probably found out, finding the right position for all nineteen numbers in the net is certainly not an easy task. There are 12 possible solutions, but in fact they are all rotation and mirror symmetrical variants of one and the same solution. This solution has a sum of 38 on any of its horizontal and diagonal rows, and is shown below:

 

Neptune

Four words add up to a fifth word numerically:

     mars
    venus
   uranus
   saturn
  -------- +
  neptune

Each of the ten letters (m, a, r, s, v, e, n, u, t, and p) represents a digit in the range 0 up to 9 (equal letters represent equal digits and different letters represent different digits). Furthermore, the digits 1 and 6 are being used most frequently.

 

Answer:

The easiest way to solve this problem is by writing a computer program that systematically tries all possible mappings from the digits onto the letters. This will give you only one solution which meets the condition that the digits 1 and 6 are most frequently used:

     mars         m = 4
    venus         a = 5
   uranus         r = 9
   saturn         s = 3
 -------- +       v = 2            4593
  neptune         e = 0           20163
                  n = 1          695163
                  u = 6          358691
                  t = 8        -------- +
                  p = 7         1078610

Complete a Word!

Fill in a letter to complete a 12-letter word reading either clockwise or counterclockwise. What is this 12-letter word?

Answer:

Correlatable (what can be correlated; e.g., correlatable phenomena).

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

What Letter?

A B C D E F G H

You have 10 seconds to identify what letter is two letters to the left of the letter immediately to the right of the letter three letters to the right of the letter A?



 

Answer:

C

MTD is to PXB as FRJ is to?

MTD is to PXB as FRJ is to?

 

Answer:

IVH: the first letter moves three places in the alphabet forwards: FghI; the second letter moves four letters in the alphabet forwards: RstuV; the third letter moves two places in the alphabet backwards: JiH.

Missing Hour Hand

Can you work out what number the missing hour hand on clock 4 should point at?

Answer:

The two numbers added together give the number the minute hand points at on the next clock. The hour hand points at the number three spaces before.

Reasoning Behind Diagram

Can you work out the reasoning behind this diagram and fill in the last square?

 

Answer:

Start at the top right and move across the square in a horizontal boustrophedon. The pattern is: miss 1 square, turn by 1800, turn by 900 clockwise, miss 1, turn by 900 clockwise, turn by 1800.

Find two eight-letter words!

Take one letter from each circle in turn and using each letter once only find two eight-letter words that are similar in meaning. Both words read clockwise and each starts in a different circle.

 

Answer:

PAMPHLET & BROCHURE

---

Publisher: iUniverse (December 13, 2012)

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

Shields

In 30 seconds only, identify which shield should replace the question mark?

Answer:

E: each line across and down contains one each of the three symbols. In each line one symbol is black, and one is upside down.

A quotation by George Deukmejian

Solve the anagram in brackets to correctly complete the quotation with a 10- letter word.

"The difference between golf and (torn veg men) is that in golf you cannot improve your lie" - George Deukmejian


 

Answer:

government

Identify the missing section!

In one minute, can you identify which of the followings is the missing section?

 

Answer:

B: start at the bottom lefthand corner square and work along the bottom row, then back along the next row up etc, repeating the numbers 38219.

Arcs

Answer:

D: to each arc, add a quarter of a circle clockwise.

Complete two eight-letter words!

Complete two eight-letter words, one in each circle, and both reading clockwise. The words are synonyms. You must find the starting points and provide the missing letters.

Answer:

ESCALATE & HEIGHTEN

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

PURE AS TUFT

PURE AS TUFT is an anagram of which two words that are opposite in meaning?

 

Answer:

PAST & FUTURE