The One With The Matematica

As promised Technothlon team is back to take the discussion further, and to more core sections. The discussion for the section, 'INGENIOSO MATEMATICA' will be on for another 2 days. There's a lot to gain from these questions. Hope to see you all commenting with your strategies, and a few shortcuts you might have discovered accidentally during the prelims.

"Juniors"

Q-1:

In the botanical garden owned by Vijay, there are three type of plants; ones which bear red flowers (I), ones which bear pink flowers (II), and rest bear both (III). Currently, the garden accommodates equal number of flowers from each category. As an effect of fertilizers, the red ones have lost their ability to reproduce and the rest two have equal chance to reproduce any of the three types, but one plant can reproduce only one plant at a time. The moment type-III plant is produced; the mother plant is treated so as to stop reproducing. If this continues for a long time, what would be the average number of child plants, that a mother plant ( type II and III) would have?

1) 1                   2) 3                  3) 2                  4) 6

Q-2:

Kanheiya has joined the summer camp, where he gets to solve some interesting problems to sharpen his brain. He has been given 2 cubes, using which he has to represent all the months and dates. Each face of a cube bears different digits (from 0-9), but the digits on the two cubes can be the same. He does that first assuming that ‘5’ will be represented as ‘5’ and not ‘05’. He then repeats the same for the case where ‘5’ is represented as ‘05’. What’s the minimum number of common faces the two cubes can have, with first cube faces adding up to give the least sum, in the two cases.

1) 2,2               2) 2,3               3) 3,3               4) 3,2

Q-3:

Megha has been selected as the Event Organizer for the upcoming Rangoli Competition in your society and has to buy 100 colour packets, using only the society fund of Rs. 100. She decides to spend all the fund for buying colours only. A red colour packet costs Rs. 6 each, a yellow one Rs. 3 and Green one for Rs 0.10. How many colour packets will she have?

(How to answer? If Megha bought 15 Red packets, 50 Yellow packets, and 35 Green packets then your answer should be: 5035 i.e. first two digits will be the number of yellow packets and the last two digits will be the number of green packets.)

Q-4:

Sanny is trying to label two wires with their capacity, which is the maximum weight it can handle. He knows that the capacity of both the wires is the same and is between 1 and 100 kg. He has 100 weights: 1kg, 2kg, 3kg, …., 100kg, to test the capacity. What is the least number of trials required by Sanny for knowing the capacity?

(How to answer? If he takes 123 trials, then answer 0123.)

Q-5:

Eight shopkeepers, who used to quarrel a lot among themselves, were given slot numbers by a fair owner as 1 to 8, such that the shopkeeper with a particular number will have his quarreling mates as his nearest numbers. The shops are separated by the roads as shown below. Now it’s the time to arrange their shops for the fair on the map such that no one will encounter his quarreling mate just next, in a row or a column or diagonally.

Sayantan, the owner has done it, can you?

(How to answer? Give the unit’s digit of all the three columns in the increasing order. Eg: if the three sums (left to right) are: 99,98,97, (which surely can’t be!) then the answer is: 0789.)

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"Hauts"

Q-6:

There are 8 teams in a tournament, and are known by their captains names. Four matches will take place to select the teams for the next level. Every team plays only once. Three umpires have predicted the following winners, and see the coincidence, all three of them are correct.

Umpire-1: Sayantan, Vijay, Ashima, and Vishal.

Umpire-2: Kanheiya, Himanshu, Ashima, and Sayantan.

Umpire-3: Anirudh, Vijay, Himanshu, and Sayantan.

None picked Greeshma. Who played with Kanheiya?

1) Anirudh                  2) Vijay                       3) Vishal                     4) none of these

Q-7:

A lunar Spaceship takes off every odd hour (1,3,5,7,...), night and day, from the Piternia launching station. Every odd hour a ship, from the moon also leaves for earth. A constant distance is maintained from one another by the spaceships, in both directions , and the speed is maintained so that they arrive at the final spot on the even hour(2,4,6,8,...). You are lucky to get a chance to go in the space shuttle, with your partner. “That’s the seventh ship we’ve passed since we left the ground.”,says the person seated by the window.

On which ship are you riding?

1) E                  2) C                3) D                4) G

Q-8:

Kushal has joined the summer camp, where he gets to solve some interesting problems to sharpen his brain. He has been given 2 cubes, using which he has to represent all the months and dates. Each face of a cube bears a unique digit(from 0-9), but the digits on two cubes can be same. He does that first assuming that ‘5’ will be represented as ‘5’ and not ‘05’. He then repeats the same for the case where ‘5’ is represented as ’05’. What’s the minimum number of common faces the two cubes can have, with first cube faces adding up to give the least sum, in 2 cases.

Q-9:

A long time ago, when the Egyptian Empire was spreading across the boundaries of Egypt; several different ethnic groups were made slaves. Over time the slave communities united and made their own Pidgin(a new language) to communicate with each other. To take revenge, the oldest members of these groups: Dhruv, Sanny, and Zilani, indulged in black magic, and cursed the oldest and the most powerful Mummy of the Dynasty and its treasure: “WARTS AKA STRAW” meaning: “2013 will see the fall of Dynasty and you would be the reason”. But the curse will show its effect only when the Mummy is re-awaken, and the one who reawakens will die. To save the Empire one must get control over the Mummy.

Now in 2013 A.D., archeologists Anirudh and Vishal visit the pyramids in search of the treasure, and come across a manuscript which asks them to find the number of ways there are, to spell, “WARTS AKA STRAW” excluding the spaces, by travelling from letter to letter in the grid. Unaware of the curse, in greed

of Treasure they accidently re-awake the Mummy, and are forced to death. You can save the Empire by getting control over the Mummy if you can find this mysterious number.

(Hint: Most probably, much more than you think.)

(Hint: Every possible path passes through the center.)

(How to answer? Answer the last four digits of your answer. Eg.: if the answer is: 0123, then mark your answer as: 0123.)

Q-10:

In a botanical garden, owned by Megha; there are three types of plants, ones which bear red flowers (I), ones which bear pink flowers (II), and rest bear both (III). Currently, the garden accommodates equal number of flowers from each category. As an effect of fertilizers, the red ones have lost the ability to reproduce, and the rest two have equal chances to reproduce any of the three types, but one plant can reproduce only one plant at a time. The moment type-III plant is produced; the mother plant is treated so as to stop reproducing. If this continues for a long time, what would be the ratio of the three types of plants in the garden?

(How to answer? If the ratio is: x:y:z (say 7:8:9) then answer xyz(0789).)

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