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  1. Mum washes clothes. She puts 3 shirts, 3 pairs of trousers and 2 blankets on the line to dry. A shirt dries in 1hr, a pair of trousers in 2hrs and a blanket in 3hrs. How long should she wait for all the clothes to dry?



  2. Few bees found a few flowers. Each bee sat on a flower and one bee did not have a flower to sit. The bees, being from the same group, got off and sat two on each flower. Now one flower had no bee on it. How many bees and how many flowers?
    [From 'Asthaana Kolaakalam' - Saraswathi Mahal (Library of Nadi's - Palm Leaves), Thanjavur, Tamilnadu, India]


  3. Fill this 3 x 3 magic square with natural numbers from 1 to 9 so that column, row and diagonal totals are all 15 each.

  4. In a playschool, each child was asked to take two number-tiles, (each bearing a single digit), from the basket and arrange as many different 2-digit numbers as possible. Most children arranged two different 2-digit numbers; Neela claimed to have arranged four; Krishna only one; and Parvathi claimed three 'two-digit numbers'. Are these claims possible? If so justify with reasoning!


  5. Find the perimeter.


    [Everyone can find it. The catch is you should find it in 2 to 5 seconds!]


  6. Santosh went with Rs.100 to buy fruits. A banana was Re.1; twenty amlas cost Re.1 and one guava was Rs.5. Santosh bought 100 fruits (including all three kinds) which cost exactly Rs.100. How many of each type of fruit did he buy?
    [From 'Asthaana Kolaakalam' ...


  7. Gopal, a rural man, was sitting on a bundle of green grass with his goat and his pet tiger, waiting to cross the river. The coracle [ghpry;] was too small and could take Gopal and only one of his belongings at a time. We all know that goat likes grass and tiger likes goat! Gopal made more than one trip but successfully transported all three belongings to the other bank. How?


  8. A group of girls found few short benches. They sat two to a bench; two girls did not get a bench. They sat three to a bench. Now a bench was extra. How many girls; how many benches?


  9. A frog caught a fly 20m away from its pond. While returning, it jumped only half the distance to the water each time. How many jumps were needed to reach the water?


  10. Another frog lived in a well whose water-level was 20.5 spans below the ground-level. The frog wanted to climb out of the well for a break. As it cimbed 3 spans, it slid down back 1 span. But it continued and eventually got out of the well. How many climbs would the frog have made?


  11. Take a single-digit nuber, say, 7. Multiply it by 9, get 63. Start with another number, say 3 and its multiple is 27. Tabulate them like this:
      7
    3
    63
    27
     
    Repeat this a few times more, if needed, taking a different single-digit number each time. Look at the results carefully; write any patterns you notice.


  12. Little Mani took any 2-digit number, say 35; he flipped the digits, got 53; their difference is 18. He wrote these in a horizontal line like this:
      35
    53
    18
     
    He wrote few more lines like this, each time starting with a new two-digit number. He looked at the 'differences' closely; he found some pattern. Can you repeat what Mani did and find the pattern?
    [You may see a few more patterns!]


  13. Mani's sister Selvi did something else. She took a special two digit number (its units digit is 1 more than its tens digit); multiplied it by 9 and wrote the result to the right of the original number. She repeated this many times each time starting with a new two digit number. When Selvi studied all the multiples she found a different pattern. Can you repeat what Selvi did and find the pattern?


  14. Kumar told Bharath that dividing any number by 7 is fun. Bharath disagreed but started to play with division of 1, 2, 3, ... by 7 and wrote the decimal answers and observed them and found an interesting pattern. By this time Kumar returned and challenged Bharath if he could divide 38 by 7 fast and write the answer. Now Bharath said that it was fun(!) and wrote the decimal answer in 2 seconds. Can you also find the pattern and write the answer dividing 65 by 7 instantly?


  15. Take a special sequence of numbers, 1, 2, 4, 8, ..., in which doubling any term gives the next term and the squence starts with 1. Find the sum of these terms, taking one term, then taking two terms, then three terms and so on. List the terms and their sums as below:
      1
    1, 2
    1, 2, 4
    1
    3
    7
     
    Shankar was serious and wrote more than seven or eight rows and started to look for any pattern. Suddenly he shouted 'eureka'. Can you also shout 'eureka' and tell the sum of the first eleven terms without actually adding?


  16. Fill this 4 x 4 magic square with natural numbers from 1 to 16 so that column, row and diagonal totals are all 34 each.
  17. 4x4 magic square



  18. A foot (12 inches) ruler is marked in 1/10 inch units. Totally how many division-marks will there be along one edge?


  19. Subramani said, "At last I know to write all the hundred names of numbers (in English words) from 1 to 100." His elder sister, Kamatchi said, "But you do not need hudred different (distinct) words for it. Count the distinct words you have used to write." How many did Subramani count?


  20. Sanjay poured 6 litres of water into his rectangular fish-tank with a base of 30cm x 20cm and height 20cm. The tank was only half full. So he agian poured 3 more litres of water. What is the depth (in cm) of water now?


  21. There was a small book-shelf with 4 shelves. Partha arranged few books on the shelf as follows: English book was immediately below Maths book. Geography was immediately below History. Maths was immediately above Science. Geography could not be at the bootom most shelf. Partha realised two books happened to be on the same shelf. Which are the books?


  22. 2x3 path grid The 2 by 3 grid shows the paths available to go from Sarathi's home to school. If he walks horizontally to the right or vertically downwards only, how many different routes are possible?


  1. Madhanika took part in a sack race. 11 lemons were kept at intervals of 1m each, the first being 5m from the 'start' point and the others were farther off. She had to run, collect the first lemon, bring it back to the start, put in a bucket; again go and collect the second and so one. How far would she run to collect all the 11 lemons?


  2. A lady selling eggs was tripped by the royal elephant and lost all eggs. She complained to the King who instructed his Manthri (Minister) to compensate her. Manthri asked the lady how many eggs she carried. The lady did not know but she knew this: When she counted
    2 by 2 she found 1 remaining;
    3 by 3 she found 2 remaining;
    4 by 4 she found 3 remaining;
    and so on and finally
    10 by 10 she found 9 remaining;
    Can you tell the manthri how many eggs did the lady carry so that he can pay her for them?
    [From 'Asthaana Kolaakalam' ...]


  3. Kumar sent '23849' as SMS, saying this was his 8-digit phone number. Can you find it?


  4. My young student Ann Mary was doing a problem in 'Combinations'. The result was
    (7C3 x 6C2) + (7C4 x 6C1) + (7C5 x 6C0)
    This becomes:
    (35 x 15) + (35 x 6) + (21 x 1).

    As Ann Mary was getting ready to 'attack' this terrible calculation, I told this is a simple mental work and the answer was 756. Could you figure out how?


  5. Raj and Ravi were friends who were selling ghee. One day they were passing through a forest to go to the town on the other side to sell ghee. They had three (irregular shaped) vessels with exact capacities of 3, 5 and 8 litres. The smaller ones were empty and largest one was full of fresh and wholesome cow ghee. Unfortunately, on the way they started to quarrel so bitterly that they decided to go separately. They, now, had to share the ghee into equal measures but they did not have any other vessel or container or measure. How would they split evenly?


  6. A wild boar runs at a speed of 20m a minute. A hunter is chasing it. But the hunter decides to run 1m the first minute, 2m the second minute, 3m the third minute and so on. After how many minutes will he catch the boar?
    [From 'Asthaana Kolaakalam' ...]
    [The method given in the palm-leave manuscript is just stunning!]


  7. The average weight of 10 boys was 63kg. Two boys weighing 56kg and 54kg left the group and two new boys weighing 48kg and 62kg joined the group. What is the new average?


  8. Priya’s maths teacher taught the class how to fill magic squares fast. She drew a Jumbo 25 x 25 square and started to fill the consecutive numbers from 1. What will be the row or column or diagonal total?


  9. 27 + 31 + 35 + ... + 63 = ? [Everyone will list all the numbers and add. That is not aptitude!]


  10. A very devout Bhaktha visits two nearby Ganapathy temples. Each temple has a tank which will double the number of flowers that are dipped in it. He gathers some flowers from the Nandavanam (Temple garden); dips them in the temple-tank while bathing; offers a few of the flowers to Ganapathy. He goes to the second temple with the left-over flowers; dips them in the tank; offers the same number of flowers to this Ganapathy also. He has no more flowers left. How many flowers did he start with and how many flowers did he offer to the Ganapathys?
    [From 'Asthaana Kolaakalam' ...]


  11. Refer to previous problem. On an auspicious day the Bhaktha visits three such Ganapathy temples. What are the answers?


  12. A 3 x 3 magic square is filled by consecutive multiples of 3 starting from 21 onwards. What will be the total of any one diagonal?


  13. A 4 x 4 magic square is filled by natural numbers from 41 downwards. What will be the total of any one column?


  14. An elephant costs 5 varaagan (gold coin); a horse costs 3/4 varaagan and a goat costs 1/4 varaagan. How many of each one should buy if he has to buy exactly 100 animals whose cost is exactly 100 varaagans?
    [From 'Asthaana Kolaakalam' ...]


  15. Little Chandhru was asked to write all the page-numbers of a little book on a paper and find their average. His friend Punitha also got interested and she also started to do the same independently. After a while, they came up with different answers: Chandhru, 37.4 and Punitha, 37.5. Which answer is more probably correct?


  16. 210 + 210 + 210 + 210 = 2?


  17. What is the sum of all odd numbers below 100?


  18. What is the sum of all even numbers upto 100?


  19. What is the area of a square of diagonal 1.414 units to the nearest whole number?


  20. What is the area of a rectangle 5 units tall and one of its diagonal measuring 13 units?


  21. One side of a right-angled triangle is 12cm. Write the other two sides. [There are more than one set of answers.]


  22. Sreenivas was writing the English names of numbers from 1 to 1000. How many distinct words did he have to use?


  23. Both Santosh and Sumit solved the problem, lady with eggs, and each got a different answer. Is there only one answer or many answers?


  24. A 5 x 5 magic square is filled with numbers from 21 onwards. What is the line, column or diagonal total?



  25. Little Mahesh wrote:
    T H R E E +
      F O U R  

    E I G H T 
      Little Selvi wrote:
    T H R E E +
      F O U R  

    S E V E N  

  26. Kali said, "Both are right!"
    Can you find the digits that will replace the letters in each case?


    Example: A 5x5 magic square filled with numbers from 1 to 25.



  1. Meenu and Swathi run around a circular track in the opposite directions. Swathi makes 2 complete rounds and Meenu makes 3 rounds in the same time. Assuming that both start together, how many times will they meet before they would meet again at the starting point?


  2. Adhith cycled to his school at a speed of 4kmph and took 42 minutes. On return, he was in a hurry. He cycled faster at the rate of 6kmph. How long would he take to return home?


  3. A 3 x 3 magic square is filled with odd numbers starting from 19. What will be a column total?
    [Can you find the answer without actually constructing a magic square, say, in about 10 seconds?]


  4. Anil Amb was going to give Rs.100 to the beggar whom he regularly sees at the trafic signal. The beggar intercepted and said, “Sir, I don’t want this today. But I would like you to give me Re.1 today and on every following day, twice the amount of the preceding day, for just 12 days.” Anil thought this was good fun and readily agreed. How much did he pay in all, in 12 days?


  5. A and B run round a circular track 800m long. A’s speed is 250m per minute ans B’s is 200m per minute. If both run in the same direction, when will they first meet again at the ‘start’?


  6. A king had three queens. Each queen had one son. One day a farmer presented the king with some tender cucumbers and the king left the basket on the table. One queen passed that side and saw the cucumbers. She divided them into three equal parts and found one piece extra. She gave it to her son; took one part and went away. After a while, another queen saw the basket. She divided the cucumbers in the basket into three parts and found one piece extra. She gave it to her son; took one part and went away. Finally the third queen saw the basket and did exactly as the other two queens. Now the king came and took the basket and distributed the cucumbers equally to the three queens. How many cucumbers were presented by the farmer?
    [From 'Asthaana Kolaakalam' - ...]


  7. Prakash walks clockwise along a circular track, 300m long, once every 3 minutes. Ramesh walks anticlockwise once every 4 minutes. What is the time between two consecutive crossings?


  8. The elephants were taken out of the fort. They had to cross 10 levels of barriers. The first barrier had one gate, the second barrier had two gates and so on and the final tenth barrier had ten gates. Now the elephants went through the first gate; they split equally and passed through each of the two gates of the second barrier; and likewise equal number of elephants passed through each gate of any barrier. Finally ten equal groups of elephants passed through each of the ten gates of the final barrier. How many elephants were there?
    [From 'Asthaana Kolaakalam' ...]


  9. 972 + 1032 = ? [in 5 to 10 secs.!]


  10. The ratio of a 2-digit number and the number obtained by reversing the digits is 17 : 5. What is the number?


  11. Find the value correct to 3 d.p. : .




  12. A 3m deep pit measuring 56m by 24m is dug in a rectangular field measuring 264m by 56m and the soil is evenly spread on the field. What is the rise in the level of the field?


  13. 39 x 40 x 41 = ?
    [In around 5 seconds!]


  14. The area of the in-circle of an equilateral triangle is 123 units2. What is the area of the circum-circle of the same triangle?


  15. A trader puts the prices up by , just 2 months before the festival season. One month before the festivals what exact discount will he offer to realise the original price?


  16. While calculating the average of some natural numbers starting from 1, one number was missed and the average worked out to be . What was the missed number and how many numbers were taken?

  17. A circle is circumscribed by an equilateral triangle. If the radius is 2cm, what is the area of the triangle?


  18. A, B & C together started a work on the 1st of October. A could have done the work alone in (1/11)th of the month. B could have done the work alone in (1/7)th of the month. C could have done the work alone in (1/13)th of the month. When will they finish the work?


  19. A lotus flower is one span above the water. Wind starts blowing. As the intensity of wind increases the flower slowly moves and just submerges in the water at a distance of 4 spans from the original position. What is the depth of the water?


  20. In an A. P., T3 + T5 + T10 = T6 + T8.
    Find n, if Tn = 0.


  21. The cost of two TV’s are in the ratio 13 : 7. The government charged a flat surcharge of Rs.15000 per TV. Now the ratio became 8 : 5. What was the cost of the economical TV before the surcharge?


  22. If Rs.8000 is invested at 7.5% p.a. for 2 years, what is the difference in the interests by S.I. and C.I. (compunded annually)?


  23. Two cylinderical candles. One is 3cm in diameter and 8.5cm long while the other is 5cm in diameter and 6.25cm long. The first one burns at the rate of 2.25cm per hour and the second one at 1.5 cm per hour. If both are kept side by side on an even surface and lit at the same time. How long after will the flames be at the same level?


  24. A peacock is perched at the top (P) of a vertical pole 8m tall. It spots a snake (S), 32m from the pole, gliding towards its hole (H) at the foot of the pole. Pouncing obliquely, the peacock picks the snake at (C). If speeds of peacock and snake are equal, how far from the foot of the pole did the peacock pick the snake?


  25. 1082


  26. In an Arithmetic Sequence, 21st term is 361 & 41st term is 701. What is the 11th term?


  27. A 54m tall tree broke at some height from the ground due to a gale and the upper portion, still attached to the trunk, fell down touching the ground at a point 36m away. At what height did the tree break?


  28. The festival season was approaching. The trader realized he had to offer discounts. So, immediately, he put new price-tags with the prices increased by 33 1/3 (thirty-three and a third) %. One month before the festivals he announced a 'grand sale'. What percentage discount would he offer, if his intention was to realize the earlier (normal) prices?


  29. A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 5 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 8 hours. What fraction of the tank (initially empty) will be filled in 2.45 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75). [whole tank]


  30. Shruti, was rowing down a river to a camp. After a while she returned to her starting place. She realizes she has taken double the time for the return. Compare Shruti's still water speed to the river's speed.


  31. What is the sum of the first 51 terms of the sequence 21, 24, 27, ... ... [say in under 10 seconds!]


  32. How many distinct (different) English words do you use to name/call numbers from 1 to 999,999?