Sharpen Your Brain

Missing Price

2013-03-03T10:29:00.000-08:00

When I went to the store, I purchased four items. The following shows the cost of three of the items:

$1.50
$3.00
$4.00

The line to the checkout was pretty long, so to quench my boredom I started playing with my pocket calculator while waiting.

I found out, to my surprise, that the four prices of the four items I purchased added to the same number as I got when I multiplied the four prices together.

What was the price of the fourth item?

Answer:

The three prices add to 1.50 + 3.00 + 4.00 = $8.50.
The three prices multiply to 1.50 x 3.00 x 4.00 = $18.00.
You might be able to see that adding another $0.50 will take the total to $9.00, and multiplying by another $0.50 will take the product to $9.00 also, but the answer can also be found using algebra. Let's call the unknown price P:

1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
8.50 + P = 18.00 x P
8.50 = 18.00 x P - P
8.50 = 17.00 x P
8.50/17.00 = P
P = 0.50.

Area of a Square!

2013-03-03T10:27:00.002-08:00

You have a piece of paper, 10cm by 10cm. Area = 100cm^2. For some reason, you need a square piece of paper with an area of 50cm^2. Using the paper you have, what's an easy way of getting the new square?

Answer:

Fold the four corners of the square into the centre. This doubles the thickness of the paper, and so halves the area.

Monk Steps

2013-03-03T10:25:00.003-08:00

A monk has a very specific ritual for climbing up the steps to the temple. First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps are there?

Answer:

There are 49 steps.

He climbs halfway, which is step 25. He hears the bird singing on step 33. He picks up the pebble on the 21st step and tosses it on the 22nd step. The remaining 27 steps are taken three at a time which is 9 paces.

How Many Campers?

2013-03-03T10:24:00.001-08:00

Camp Pineveiw's cook, Margaret Johnson, was just about to begin preparing the picnic lunch for all the campers. She already knew she needed to fill 55 bowls of the same size and capacity with the same amount of food. When she was done, she decided to read the guidelines for the picnic, just out of curiosity. The guidelines said:

1. Every camper gets their own bowl of soup.
2. Every two campers will get one bowl of spaghetti to share.
3. Every three campers will get one bowl of salad to share.
4. All campers are required to have their own helping of salad, spaghetti, and soup.

After some rapid calculations, Margaret was able to figure out how many campers were going to the picnic. Can you?

Answer:

30 campers.

Troubling Doubling at School

2013-03-03T10:21:00.003-08:00

Read the little poem and answer its question if you can.

The number of girls who do wear a watch
is double the number who don't.
But the number of boys who do not wear a watch
is double the number who do.
If I tell you the number of girls in my class
is double the number of boys,
Can you tell me the number I teach? Here's a clue:
More than 20; below 32!

Answer:

27

Solution:

The number of boys must be a multiple of 3 (3, 6, 9...) so that it can be split in the ratio of 2:1 (no watch:watch).
The number of girls is double the no. of boys (6, 12, 18...)
So the totals can only be 9, 18, 27...

Reindeer

2013-02-24T14:27:00.002-08:00

Santa always leaves plans for his elves to determine the order in which the reindeer will pull his sleigh. This year, for the European leg of his journey, his elves are working to the following schedule, that will form a single line of nine reindeer:

Comet behind Rudolph, Prancer and Cupid. Blitzen behind Cupid and in front of Donder, Vixen and Dancer. Cupid in front of Comet, Blitzen and Vixen. Donder behind Vixen, Dasher and Prancer. Rudolph behind Prancer and in front of Donder, Dancer and Dasher. Vixen in front of Dancer and Comet. Dancer behind Donder, Rudolph and Blitzen. Prancer in front of Cupid, Donder and Blitzen. Dasher behind Prancer and in front of Vixen, Dancer and Blitzen. Donder behind Comet and Cupid. Cupid in front of Rudolph and Dancer. Vixen behind Rudolph, Prancer and Dasher.

Can you help the elves work out the order of the reindeer?

Answer:

Prancer
Cupid
   Rudolph
    Dasher
     Blitzen
      Vixen
       Comet
        Donder
         Dancer

Ten Horses

2013-02-23T14:01:00.004-08:00

How can you get ten horses into nine stables, one per stable?

Answer:

Place one letter from TEN HORSES into each of the nine stables.

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

A line through all of the edges

2013-02-23T13:56:00.000-08:00

Can you draw a line through all of the edges in this picture?

Each side is broken into 2 or 3 edges, and there are also 7 edges inside that you have to cross. The line must be continuous, and cross each edge exactly once.

Answer:

There is no possible way to complete the line, there will always be one edge left - or you have to cross an edge twice. This puzzle is the same as the famous 'Seven Bridges of Konigsberg' problem first solved by Euler. In that problem, the task was to find a closed path that crossed each of the seven bridges of Konigsberg (now Kaliningrad, Russia) exactly once.

Create Two Longer Words

2013-02-23T13:37:00.000-08:00

Can you place a common 4-letter word into each of the brackets to create two longer words, for example:

Question - COOK [....] CASE
Answer   - COOK [BOOK] CASE
The word BOOK creates the words COOKBOOK and BOOKCASE.

DRIFT   [....] WIND
HOME    [....] BENCH
FOOT    [....] MOTHER
JUNK    [....] STICK
MOTH    [....] ROOM
QUARTER [....] GROUND
SPACE   [....] YARD
WILD    [....] BOAT
YOUR    [....] LESS
BACK    [....] FIGHTER

Answer:

DRIFT   [WOOD] WIND
HOME    [WORK] BENCH
FOOT    [STEP] MOTHER
JUNK    [YARD] STICK
MOTH    [BALL] ROOM
QUARTER [BACK] GROUND
SPACE   [SHIP] YARD
WILD    [LIFE] BOAT
YOUR    [SELF] LESS
BACK    [FIRE] FIGHTER

Arrow

2013-02-23T13:34:00.001-08:00

Consider an arrow in flight towards a target.

At any given moment of time, a snapshot could be taken of this arrow. In this snapshot, the arrow would not be moving. Let us now take another snapshot, leaving a very small gap of time between them. Again, the arrow is stationary. We can keep taking snapshots for each moment of time, each of which shows the arrow to be stationary. Therefore the overall effect is that the arrow never moves, however it still hits the target!

Where lies the flaw in the logic?

Answer:

The arrow clearly reaches the target.

This is a classic paradox, attributed to Zeno of Elea, a Greek philosopher from Italy. Great minds over the centuries have pondered this paradox, and the scope of a solution is beyond the space available here. It is not even clear that a solution to the paradox actually exists.

For more information, visit the Wikipedia article on Zeno's paradoxes.

Prisoner

2013-02-23T13:31:00.005-08:00

Imagine a prisoner in a prison. He is sentenced to death and has been told that he will be killed on one day of the following week. He has been assured that the day will be a surprise to him, so he will not be anticipating the hangman on a particular day, so keeping his stress levels in check.

The prisoner starts to think to himself, if I am still alive on Thursday, then clearly I shall be hanged on Friday, this would mean that I then know the day of my death, therefore I cannot be hanged on Friday. Now then, if I am still alive on Wednesday, then clearly I shall be hanged on Thursday, since I have already ruled out Friday. The prisoner works back with this logic, finally concluding that he cannot after all be hanged, without already knowing which day it was.

Casually, resting on his laurels, sitting in his prison cell on Tuesday, the warden arrives to take him to be hanged, the prisoner was obviously surprised!

Ponder this...

Answer:

This puzzle is a classic paradox. You are led through a sequence of seemingly valid arguments which lead to a conclusion, which quite clearly cannot be true.

Cube Views

2013-02-18T00:15:00.002-08:00

Here is a cube presented from five different perspectives. One of the views is incorrect. Can you tell which one?

Answer:

View C is not correct.

Cape of Good Hope

2013-02-16T22:02:00.004-08:00

The weather at the Cape of Good Hope makes it a notorious location where many ships have been lost to the sea. Philip Wood, the famous diver, has discovered four ships that sank in the same spot, one on top of each other.
With some skill, Philip was able to determine the name, captain, cargo, destination and year each ship was built. The question is, can you?

1. During his first exploration of the site, Philip determined there were four ships - the Red Rover, the ship built in 1743, the ship captained by Quigley and the ship carrying tea that was bound for North America.
2.The ship that carried a cargo of saffron was built after the ship that carried a cargo of tea.
3. An entry in one ship's log found at the site indicated that the ship built in 1522 was carrying a valuable cargo of gold.
4. One ship was carrying botanical specimens to France. Philip determined that this was not the Royal Bride.
5. The Scarlet Queen, a pirate ship, was certainly built before the nineteenth century but not as early as the sixteenth. The captain of this ship was the famous rogue Clubfoot.
6. The Wanderer was built after the Royal Bride. The Royal Bride's cargo was not tea and the Royal Bride was not travelling to the South Seas.
7. Captain Bolton's ship was built before Clubfoot's and before The Royal Bride.

Ships: Red Rover, Royal Bride, Scarlet Queen, Wanderer
Year Built: 1522, 1688, 1743, 1817
Captain: Bolton, Clubfoot, Quigley, Vickers
Cargo: Gold, Saffron, Specimens, Tea
Destination: England, France, North America, South Seas

Answer:

Name           Year Captain   Cargo      Destination
Royal Bride    1743 Vickers   Saffron    England
Scarlet Queen 1688 Clubfoot Tea        North America
Red Rover      1522 Bolton    Gold       South Seas
Wanderer       1817 Quigley   Specimens France

The ship built in 1522 was carrying gold (3). This is not the Scarlet Queen (5), the Wanderer (6) or the Royal Bride (7) so must have been the Red Rover. The Scarlet Queen was built in either 1688 or 1743 (5) and the Wanderer was built after the Royal Bride so the Wanderer was built in 1817 and the Royal Bride in either 1688 or 1743 so the captain of the Red Rover was Captain Bolton (7). The ship carrying tea was not the Red Rover (gold), the Royal Bride (6) or the Wanderer (2) so was the Scarlet Queen. The Scarlet Queen's destination was North America (1) and her captain was Clubfoot (5). The Scarlet Queen was not built in 1743 (1) so was built in 1688 and the Royal Bride was built in 1743. The Royal Bride was not carrying gold (Red Rover), tea (Scarlet Queen) or botanical specimens (4) so was carrying saffron and the Wanderer was carrying the specimens to France. Quigley was not the captain of the Royal Bride (1) so was the captain of the Wanderer and Vickers was the captain of the Royal Bride. The Royal Bride's destination was not the South Seas (6) so was England and the Red Rover's destination was the South Seas.

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

A Brain Teaser

2013-02-16T21:58:00.004-08:00

This is a brain teaser:

What is represented by this BrainBat?

FIZZ FIZZ FIZZ FIZZ FIZZ FIZZ

Answer:

Physics (fizz x 6)

Build a Tower

2013-02-16T21:53:00.000-08:00

Imagine that you are building a tower of play bricks.

A yellow brick is 19 millimetres tall and a green brick is 21 millimetres tall.

How many of each are required to build a tower that is exactly 562 millimetres tall?

Answer:

13 yellow and 15 green bricks.
We are after Y lots of 19 plus G lots of 21 to equal 562.
    19Y + 21G = 562
It is easiest to try different values for Y, until one gives an answer divisible by 15:
    21G = 562 - 19Y
Y = 1 >> 21G = 562 - 19 = 543   x
Y = 2 >> 21G = 562 - 38 = 524   x
Y = 3 >> 21G = 562 - 57 = 505   x
Y = 4 >> 21G = 562 - 76 = 486   x
Y = 5 >> 21G = 562 - 95 = 467   x
Y = 6 >> 21G = 562 - 114 = 448   x
Y = 7 >> 21G = 562 - 133 = 429   x
Y = 8 >> 21G = 562 - 152 = 410   x
Y = 9 >> 21G = 562 - 171 = 391   x
Y = 10 >> 21G = 562 - 190 = 372   x
Y = 11 >> 21G = 562 - 209 = 353   x
Y = 12 >> 21G = 562 - 228 = 334   x
Y = 13 >> 21G = 562 - 247 = 315   OK
Y = 13, therefore G = 315 ÷ 21 = 15.

Four Bungalows

2013-02-16T21:49:00.003-08:00

There are four bungalows in our cul-de-sac. They are made from these materials: straw, wood, brick and glass.

Mrs Scott's bungalow is somewhere to the left of the wooden one and the third one along is brick.

Mrs Umbrella owns a straw bungalow and Mr Tinsley does not live at either end, but lives somewhere to the right of the glass bungalow. Mr Wilshaw lives in the fourth bungalow, whilst the first bungalow is not made from straw.

Who lives where, and what is their bungalow made from?

Answer:

From, left to right:
#1   Mrs Scott           - glass
#2      Mrs Umbrella     - straw
#3         Mr Tinsley    - brick
#4            Mr Wilshaw - wood
If we separate and label the clues, and label the bungalows #1, #2, #3, #4 from left to right we can see that:
a. Mrs Scott's bungalow is somewhere to the left of the wooden one.
b. The third one along is brick.
c. Mrs Umbrella owns a straw bungalow
d. Mr Tinsley does not live at either end.
e. Mr Tinsley lives somewhere to the right of the glass bungalow.
f. Mr Wilshaw lives in the fourth bungalow
g. The first bungalow is not made from straw.
By (g) #1 isn't made from straw, and by (b) nor is #3. By (f) Mr Wilshaw lives in #4 therefore by (c) #2 must be straw, and Mrs Umbrella lives there.
Therefore by (d) Mr Tinsley must live in #3, which, by (b) is the brick bungalow.
By (a) #4 must be wooden (otherwise Mrs Scott couldn't be to its left) and by (f) Mr Wilshaw lives there.
Which leaves Mrs Scott, living in #1, the glass bungalow.

New Word

2013-02-09T11:56:00.000-08:00

These words can all have a letter added and then be rearranged to make a new 5-letter word. The letters added spell a 9-letter word. What are the new words?

HERB
BANG
KEEN
SUIT
QUAD
WHEY
CELL
TOIL
WILD

Answer:

BERTH, BEGAN, KNEEL, SUITE, SQUAD, CHEWY, CELLO, PILOT, WIELD. The added letters spell TELESCOPE.

HERB + T becomes BERTH
BANG + E becomes BEGAN
KEEN + L becomes KNEEL
SUIT + E becomes SUITE
QUAD + S becomes SQUAD
WHEY + C becomes CHEWY
CELL + O becomes CELLO
TOIL + P becomes PILOT
WILD + E becomes WIELD

Four Days

2013-02-09T11:53:00.002-08:00

Can you name four days which start with the letter "T"?

Answer:

Tuesday, Thursday, today, and tomorrow!

Dark Room

2013-02-09T11:51:00.002-08:00

If you are in a dark room with a candle, a wood stove and a gas lamp. You only have one match, so what do you light first?

Answer:

The match!

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

AAEEIIMMPPTT

2013-02-09T11:49:00.000-08:00

Using the letters AAEEIIMMPPTT complete this grid with valid words. The grid reads the same across as down.

Answer:

The words are limp, idea, meat, pate.

Q1-Q5

2013-02-09T11:47:00.001-08:00

Here is snippet of section A of the curious multiple-choice entrance exam into the exclusive Sharpen Your Brain puzzle club.

1. The first question with B as the correct answer is:

A. 1
B. 4
C. 3
D. 2

2. The answer to Question 4 is:

A. D
B. A
C. B
D. C

3. The answer to Question 1 is:

A. D
B. C
C. B
D. A

4. The number of questions which have D as the correct answer is:

A. 3
B. 2
C. 1
D. 0

5. The number of questions which have B as the correct answer is:

A. 0
B. 2
C. 3
D. 1

Answer:

1. C
2. D
3. B
4. C
5. B
A nice, complicated, and sometimes confusing puzzle.
Step 1
Question 1 can't be A, as this would mean that Q1 was the first question with B as the answer and therefore contradict itself.
Q1 can't be B as this would mean Q4 was the first question with B as the answer, but Q1 would actually be the first question with B as the answer.
If we test Q1 as having answer C, you'll see that Q3 points back to Q1 correctly and is logically consistent. This is a possibility.
If we test Q1 as having answer D, then Q2's answer is B, which points to Q4's answer being A, which means that there are 3 questions with D as the answer. Which would mean that Q3 and Q5 were both D, but Q3 would have to be A, as we're testing that Q1 is D.
Therefore Q1 has answer C. Since Q1 has answer C, we know Q3 has answer B.
Step 2
Looking at Q4 (how many questions can have D as the answer), clearly it can't be D (zero), as this would contradict itself. It can't be A (three) as we only have 2 questions without an answer.
If Q4 was B, then the remaining questions (Q2 and Q5) would both be D, which would make Q2 point to Q4 having C as an answer, which contradicts our guess of Q4 being B.
So Q4 must be C.
Which means that Q2 has answer D.
Which means that Q5 has answer B (as no other option is allowed and we must have two questions with answer B). QED!

BrainTracker

2013-02-02T17:05:00.003-08:00

Using the BrainTracker grid below, how many words can you find? Each word must contain the central B and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. There is at least one nine letter word.
Excellent: 24 words.
Good: 17 words.
Average: 12 words.

Answer:

Common words: airbrush, bar, bars, bash, bias, brash, briar, briars, brush, burr, burrs, bursar, bus, bush, HAIRBRUSH, hub, hubs, rib, ribs, rub, rubs, shrub.

All words: ab, abri, abris, abs, airbrush, airbus, arb, arbs, ba, bah, bar, bars, bas, bash, bi, bias, birr, birrs, bis, brash, briar, briars, bris, brr, brush, buhr, buhrs, bur, bura, buras, burr, burrs, burs, bursa, bursar, bus, bush, habu, habus, HAIRBRUSH, hub, hubris, hubs, isba, rib, ribs, rub, rubs, sab, sabir, sahib, shibah, shrub, sib, sub, suba, subah, urb, urbia, urbias, urbs.

Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower

More than 20 pupils!

2013-02-02T17:02:00.001-08:00

A local school teacher wanted to share 703 sweets equally between the pupils, if there were more than 20 pupils, how many sweets did each receive?

Answer:

19 sweets for the 37 pupils.

15 well-known five letter words

2013-02-02T16:59:00.002-08:00

Below you will find 15 well-known five letter words, with only their endings remaining. In 30 seconds, can you determine the words?

..PAY
..LAD
..IOR
..EUE
..RVA
..DAY
..VOC
..YSS
..GUN
..PTY
..TIL
..CAY
..UKE
..UZE
..NOE

Answer:

..PAY >> REPAY
..LAD >> SALAD
..IOR >> PRIOR
..EUE >> QUEUE
..RVA >> LARVA
..DAY >> TODAY
..VOC >> HAVOC
..YSS >> ABYSS
..GUN >> BEGUN
..PTY >> EMPTY
..TIL >> UNTIL
..CAY >> DECAY
..UKE >> FLUKE
..UZE >> GAUZE
..NOE >> CANOE

Can you find 10 countries?

2013-02-02T16:57:00.001-08:00

During the recent BrainBashers cipher convention, a binary code contest took place. The contest consisted of a binary code transmission where the spaces between the letters were missing and there was no punctuation. Each letter of the alphabet was translated into its binary equivalent based on its position in the alphabet, a=1, b=10, c=11, d=100, e=101, f=110, g=111, h=1000, i=1001, j=1010, k=1011, l=1100, m=1101, n=1110, o=1111, p=10000, q=10001, r=10010, s=10011, t=10100, u=10101, v=10110, w=10111, x=11000, y=11001, z=11010. Can you find 10 countries?

101011000011110
101111110010110011
100001111110011110100
110100101111011101
11100010011100101
1101111110010111111111111
11010111011010011
10100110011011111110
1000011110111011
1101111111101111111110010011

Answer:

Japan, Wales, Poland, France, Chile, Morocco, Zambia, Taiwan, Panama, Mongolia.