The Hiker's Dilemma

A hiker comes across an intersection where three roads cross. He looks for the sign indicating the direction to his destination city. He finds that the pole carrying three city names and arrows pointing to them has fallen. He picks it up, considers it, and pops it back into place, pointing out the correct direction for his destination. How did he do it?

This is how he did it!

Hiker Got The Right Direction

What was the dilemma? 

Since he knew very well from which city he came; he just oriented that arrow in right direction. And obviously hence rest of all arrows are pointed in the right directions as well. This is how he found his right way!

A Fractional Pink Shade

What fraction of this figure is shaded with the pink color?

Get the answer here!


Author : Ed Southall of Solve My Maths

Area Of A Fractional Pink Shade

A look at the question first!

Let's first recall the formula for the calculation of area of a triangle.

Area of triangle =  1/2 x Base x Height

Let's assume the side of the square is 1.

Now the triangle with the pink shade & triangle opposite to it are similar triangles. Similar triangles are triangle whose sides are in proportion with each other.

Since here base of pink triangle is double of un shaded opposite triangle, the height of pink triangle must be double of that smaller triangle.

But together, heights of both triangles must be equal to side of the square i.e. 1.

And hence, height of smaller triangle must be 1/3 & that of pink 2/3. (h + 2h = 3 ; h = 1/3).

So,

Area of Pink Triangle = 1/2 x Base x Height = 1/2 x 1 x 2/3 = 1/3.

So the area of pink shaded part is 1/3rd of total area occupied by square.



 

Tricky Logical Mathematical Puzzle

Can you solve this?

 
Do you too think answer is 19 or 26 ? Here is the right one!

Answer of Tricky Logical Mathematical Puzzle

Or a look at the question itself?


Let's look at the puzzle once again.

From first equation, it is clear that figure = 15. But the figure itself made up of square (4 sides) + polygon (5 sides) + hexagon (6 sides) = 15.

From second equation, we have bunch of 4 bananas = 4 i.e. 1 banana = 1.

And from third equation, we have 3 hours in clock = 3 i.e. 1 hours  = 1.

Hence, in fourth equation, value of clock = 2, 3 bananas = 3, figure = sides of hexagon + sides of pentagons = 6 + 5 = 11.

2 + 3 + 3 x 11 = 38

Hence, answer is 38. 

Wish Of Cigarette Smoking

Bruce is an inmate at a large prison, and like most of the other prisoners, he smokes cigarettes. During his time in the prison, Bruce finds that if he has 3 cigarette butts, he can cram them together and turn them into 1 full cigarette. Whenever he smokes a cigarette, it turns into a cigarette butt.

One day, Bruce is in his cell talking to one of his cellmates, Steve.

“I really want to smoke 5 cigarettes today, but all I have are these 10 cigarette butts,” Bruce tells Steve. “I’m not sure that will be enough.”

“Why don’t you borrow some of Tom’s cigarette butts?” asks Steve, pointing over to a small pile of cigarette butts on the bed of their third cellmate, Tom, who is out for the day on a community service project.

“I can’t,” Bruce says. “Tom always counts exactly how many cigarette butts are in his pile, and he’d probably kill me if he noticed that I had taken any.”

However, after thinking for a while, Bruce figures out a way that he can smoke 5 cigarettes without angering Tom. What is his plan?

That's his master plan!

Fulfilling The Wish Of Cigarette Smoking

What was the challenge? 

Bruce takes 9 of his 10 cigarette butts and make 3 cigarettes using those 9 (9/3=3). Now, he smokes all 3 cigarettes. At this point, he has 3 + 1 = 4 cigarette butts.

Using 3 out of 4 cigarette butts, he make one another cigarette and smokes it. Now he has 1 + 1 = 2 cigarette butts & till now has smoked 4 cigarettes.

Now he borrows 1 Tom's cigarette butts making total number of cigarette butts equal to 3. Using these 3 butts he makes one more cigarette and this way he smokes 5th cigarette. 

After smoking this 5th, he puts back the cigarette butt left in Tom's pile so that Tom won't find anything missing.

Which way is the bus going? Left or Right?

Can you guess in which direction this bus is going?

Are you in the right direction?

Bus is Moving In 'This' Direction!

Why dirction was asked to find? 


Well, it totally depends on the location of the bus. How? Read further.

If you look at it carefully, then you can notice that the doors of the bus are missing.
That clearly indicates, those must be on the other side of bus.

Hence if bus is on the roads of India then it must have doors at it's left side & hence the bus must be moving in the right direction.

While in some countries, bus might have doors at the right; in the case the bus must be moving in left direction. 

Viral Maths Problem Confusing Students & Parents

There are 73 red, blue and green marbles in a jar. There are twice as many red marbles as blue marbles. There are 19 more marbles than green marbles. 

How many green marbles are there?

Check if you are correct! 

Solution of Viral Maths Problem Confusing Students & Parents

What was the problem?

Using Algebra : 

Let r,b and g be the numbers of red, blue and green marbles in the jar.

There are 73 red, blue and green marbles in a jar.

So r + b + g = 73    .....(1)

There are twice as many red marbles as blue marbles.

r = 2b                  ......(2)

There are 19 more blue marbles than green marbles. 

b = g + 19            

g = b - 19            ......(3)

Putting (2) and (3) in (1), gives

2b + b + b - 19 = 73

4b = 92

b = 23

Putting b = 23 in (3) gives,

g = 23 - 19 = 4

Putting  b = 23 in (2), gives 

r = 2x23 = 46

So there are 46 red,23 blue and 4 green marbles in the jar.

Without Algebra :

In the case, we need to try trail and error method.

If g = 1, then b = 20 and r = 2(20) = 40 giving total 40 + 20 + 1 = 61.

If g = 2, then b = 21 and r = 2(21) = 42 giving total 42 + 21 + 2 = 65.

If g = 3, then b = 22 and r = 2(22) = 44 giving total 44 + 22 + 3 = 69.

Total is increasing at the rate of 4. So finally,

If g = 4, then b = 23 and r = 2(23) = 46 giving total 46 + 23 + 4 = 73.


So there are 46 red,23 blue and 4 green marbles in the jar.

The Buyer Who is Thief

Once a man steals Rs.100 note from the shop. Later he purchases good of worth Rs.70 from the same shop using that note. The shopkeeper gives back Rs.30 in return. 

How much did shopkeeper loose in the case?


Do you think Rs.130? Or anything else? 

Loss Due To Thief Buyer

What's the case history? 

So did you just answer Rs.130 ? No, that's not correct!

Thief initially steals Rs.100 note. Now imagine instead of Rs.100 he steals goods of worth Rs. 70 + Rs.30 (given by shopkeeper). So eventually, the shopkeeper lost only Rs.100 in the process. 

In other words, the thief exchanges Rs.70 with the goods in the case. He pays for those goods to shopkeeper. So he looses Rs.70 from stolen Rs.100 & gains back via goods.

So eventually, the shopkeeper lost only Rs.100 in the case.

 

The Exact Age?

Tommy: "How old are you, Mamma?"

Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."

Tommy: "That's a lot, isn't it? And how old are you, Papa?"

Papa: "Just six times as old as you, my son."

Tommy: "Shall I ever be half as old as you, Papa?"

Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."

Tommy: "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..."

Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."

Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of Mamma?

Here is CALCULATION of exact age!

Calculation Of The Exact Age

What was the problem? 

Let us suppose T be the age of Tommy, M be of the Mamma and P be that of Papa.

Sum of their ages is 70.

T + M + P = 70  ......(1)

and Papa is 6 times as old as Tommy,

P = 6T  .....(2)

In unknown number of years X, Papa will be twice old as Tommy,

P + X = 2 (T + X)  ....(3)

and the sum of ages at that time is 70 x 2 = 140,

(T + X) + (P + X) + (M + X) = 140.

T + P + M + 3X = 140

From (1), above equation becomes,

70 + 3X = 140

X = 70/3     .....(4)

Putting (4) and (2) in (3),

P + X = 2 (T + X) 

6T + 70/3 = 2(T + 70/3)

T = 70/12    .....(6)

Using (6) in (2),

P = 6T

P = 6(70/12)

P = 70/2    ......(7)

Putting (6) and (7) in (1),

M = 70 - 70/2 - 70/12

M = 29.1666 = 29 years 2 months.

P = 70/2 = 35 years.

T = 70/12 = 5.8333 = 5 years 10 months.

 
To summarize, the Tommy is 5 years 10 months old, Mama is 29 years 2 months old and Papa is 35 years old.

50th Fastest And The 50th Slowest

Matt is the fiftieth fastest and the fiftieth slowest runner in his school.

Assuming no two runners are the same speed, how many runners are in Matt’s school?

Find here total number of runners! 

Total Runners In The School

Read the given data first!
 
This could be very tricky one. Let's assume that the Matt is fifth fastest and fifth slowest runner in his school.

Then there are 4 runners ahead of him numbered 1 to 4 and 4 behind him numbered 6 to 9. So there would be total 9 runners in his school in the case.

But Matt is 50th fastest runner meaning 49 are ahead of him numbered 1 to 49. And 49 are behind him numbered as 51 to 99 (total 49) while Matt is at 50th position.

Hence, there are 49 + 1 + 49 = 99 runners in his school.

A Rich Earl And Swamp

A rich earl has become the owner of a piece of land, which to his dissatisfaction turned out to be nothing more than a big swamp. The earl wants to get rid of the swamp. 

A salesman advises him to use his fast-growing plants which can cover the swamp very quickly. "This plant doubles every day, tomorrow you will have two, the day after tomorrow four, etc. In 80 days, your swamp will be completely covered." The earl reacts: "80 days? This takes far too much time. Then just give me eight of these plants."

Question 1: What did the earl think?

Question 2: And what do you think?

Go to the answers directly!

Planting Trees Covering Swamp

What's the exact story? 

The earl must have thought that planting 8 trees on first day itself would cause him to wait for only 10 days. That's totally wrong conclusion.

Though started with 8 trees, on other day number will be doubled only not tripled or increased to x8. Starting with 8 trees is like skipping 3 days (2,4,8) if started with 1 tree.That is only 3 days would be saved. 

In short, with 8 plants, the earl need to wait for 77 days!