### #1 - Nine Numbers Picture Puzzle

In the figure given with this question, place the numbers from 1 to 19 in the circles in a manner that each side of the triangle sums up to 17.

In the figure given with this question, place the numbers from 1 to 19 in the circles in a manner that each side of the triangle sums up to 17.

A poor villager grows mango in his land and sells them in the town. The town is 1000 miles away from the village. He has rented a truck for transporting the mangoes to the town. The truck can carry 1000 mangoes at one time and this season, he was able to yield 3000 mangoes.

There is a problem. At each mile till the town, there is a check post at which he must give one mango each while travelling towards the town. However, if he is travelling from the town towards his village, he won’t have to give anything.

Tell a way in which the villager can take highest possible number of mangoes to the town.

First of all, he will have to make three trips of 1000 mangoes till 333 miles. After that, he will be left with 2001 mangoes and 667 more miles to go.

Then he must take two trips of 1000 mangoes covering 500 miles more. Doing this, he will be left with 1000 mangoes and 167 remaining miles to reach the town. (He will have to leave a mango behind)

Lastly, he will have to travel the rest of 167 miles with the remaining 1000 mangoes and by the time he reaches town, he will be left with 833 mangoes.

While boarding a bus you notice that there are 7 girls in the bus already. All the girls have 7 bags each. In each bag there are 7 adult cats. Each of the adult cat have 7 little one. Each of the cat has 4 legs.

Can you calculate the number of legs in the bus?

Every girl has seven bags comprising of seven adult cats each with seven little cats per adult cat.

Thus for one girl:

1 girl + 49 adult cats + 343 little cats

Since there are 7 girls:

7 girls + 343 adult cats + 2410 little cats

Now calculating the legs:

14 legs of girls + 10976 legs of cats (There are total 2744 cats with 4 legs each).

Thus total legs = 10990

Now I climbed aboard the bus as well, thus total number of legs = 10990 + 2 = 10992 legs

If we add two legs of the driver as well,

Total legs = 10992 + 2 = 10994

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).

(a) If 15 matches are played in total, how many players participated?

(b) If 50 players took part in the tournament, how many matches were played?

(a) If you look at the question closely, it is a knockout tournament and the winner will be just one. Thus no. of players is equal to 15+1=16.

(b) The number of matches will always be one less than the number of players (in knockout tournaments). Thus the answer is 49.

using four eights (8) and a one (1) and one mathematical symbol , create the number 100

188 - 88

There has been a house on fire. The fireman is now standing in the middle rung of the ladder and trying to extinguish the fire. He climbs 6 rungs more but the heat and deadly flames make him climb down 10 rungs. When the fire is settling gradually, he climbs 18 rungs and reaches the top of the ladder for better access to the house.

Calculate the number of rungs in the ladder ?

29 rungs

Suppose he is standing on m at first which is the middle rung.

He climbs 6 rungs which makes his position to be m+6.

He climbs down ten rungs which makes his position to be (m+6-10) = m-4

He climbs 18 rungs to reach the top t which makes his position (m-4+18) = m+14

Now, m+14 = t

Which means there are 14 rungs above the middle rung and 14 rungs below the middle rung. Counting the middle rung as well, it makes a total of 29 rungs.

A car M starts from point A and a car N starts from point B and move towards opposite sides at a constant speed. The cars meet 500 yards from A for the first time. After reaching the opposite points, each of the car returns back without any break and this time, they meet 300 yards from B.

What is the distance between the two points A and B and what is the relation between the speeds of the two boats?

When the cars first meet, they have traveled a combined distance equal to the 1 length of the distance. When they meet the second time, they have travelled 3 lengths.

The elapsed time and distance for each of the cars is three times. Now when they meet the second time, M has traveled 500x3 = 1500 yards and since, it is 300 yards longer than the total distance between both the points, the distance is 1200 yards.

The ratio of M’s speed to the ratio of N’s speed is equal to the distance that they traveled before they met for the first time.

i.e. 500/(1200 – 500) = 5/7

A train leaves from point A for point B at 80 mph. After half an hour, another train leaves from point B for point A at 60 mph.

Which of the trains will be further from point A when they meet ?

When the trains meet, they will be approximately be equally distant from point A. Of course if you get into precise details, the train that left from point A will be closer to A by its own length as they are coming from different directions.

Emily learnt how to ride a horse recently. Just to test her skills, she rode the horse from her home till a mine which she covered in three minutes and returned back home from the same path only this time she took four minutes. The reason was that while riding away from home, she was supported by wind however while riding back, she was riding against the wind.

How fast do you think she could have rode a mile if there was no wind ?

3 minutes and 25 5/7 seconds.

The most common way how most of people see this problem is adding 3 and four to obtain 7 and they believe it should give a correct average and thus her time should be taken to 3 and half minutes. But if you do like that, you will get to a wrong answer. This is because, the wind has only helped her for three minutes while it has worked against her for four minutes.

If she could ride a mile in three minutes with the wind, it is evident that she could go a mile and 1/3 of a mile in four minutes. Thus two and 1/3 miles in eight minutes will give her actual speed as the wind has helped her as much as it has worked against her.

Thus her actual time for a single mile without wind will be 3 minutes and 25 5/7 seconds.

The below figure consists of a rectangle and the numbers labeled over the top represents the area of that particular shaded region.

Calculate the area of the green region labeled as '?'

The White triangle is similar to the Red triangle

As ratio of areas = ratio of bases when height is same,

Ratio of sides is 2:3

White triangle = 9/4 * Red triangle = 9/2

Thus the Green Region = 5.5 units.