Enjoyable questions and problems

If you see the marks students get in a subject in your class, you will find that the largest number of people get average marks, while the number of those getting higher than the average gradually reduces. Similarly, the number of those getting less than average also reduces as you move away from the average. When teachers make a graph of the marks earned by the class, they get something that looks like this:                                                                     Image Credit: Monika Wahi,  CC-BY-SA-4.0 ,                                      Image from Wikimedia Commons In this example, we assume that D is the average score 50%. Other points are: A             20% B             30% C             40% E             60% F             70% G            80% The height above each letter shows how many people got that many marks: 2 students got 20%, 5 students got 30%, 7 students got 40%, 8 students got 50% 7 students got 60%, 5 students got 70%, and 2 students got

Julius Caesar adopted a tricky method of sending messages to his generals through messengers. What if his enemies caught hold of the messenger and read the message? They will then know Caesar’s plans. Caesar’s trick was to change the letters in the message. For instance, he could write “D” instead of “A”, “E” instead of “B” and so on. Every letter would be replaced by another three places further down in the alphabetical order. What do you do with “Y”? What is three places beyond “Y”? The trick is to think of the letters being arranged in a ring so that “A” follows “Z” and “B” follows “A”. In this ring you can go three places from “Y” and find “B”. The letter three places ahead of “Z” will be “C”. To encipher a message, that is to make it secret, we first choose a key. I recommend that you choose a whole number between 1 and 6 as the key. Suppose you choose 3 as the key. Now replace every letter in “TEXT” by one which is 3 steps away along the ring. Do you get “WHAW”? You can send

Have you seen 2 3 , 3 5 and so on? Why are 3 and 5 sitting at a different level? It is just mathematicians’ shorthand: 2 3 is nothing but 2 x 2 x 2 =   8 3 5 means 3 x 3 x 3 x 3 x 3 = 243 We read 2 3 as 2 to the power 3, and 3 5 as 3 to the power five. What is 2 5 ?   Write it down. What is 2 3 x 2 5 ?   One surprising thing is that 2 3 x 2 5 = 2 8 = 256 Numbers sitting one level higher are called exponents. The exponent notation makes it very easy to write some big numbers. Try writing a million, billion and trillion! But with exponent notation, it is much easier to write them and remember them. Number In decimal notation In exponent notation Million 1,000,000 10 6 Billion 1,000,000,000 10 9 Trillion 1,000,000,000,000 10 12 Did you notice it? Million has six zero’s and is 10 6; billion has nine zero’s and is 10 9 ; trillion has twelve zer

  Nellie Bly. Photo Credit: Wikipedia Girls are as smart as boys. They may be smarter in some ways, like understanding people and in helping them. They may not be as good in fighting. In the old days, men controlled the world through hand-to-hand fighting and fighting with sticks and swords. However, times have changed. Women can now do most of the work men can. However, many countries do not allow girls to go to college or even high school. They do not allow women to work in offices. Such prejudice against women was there even in countries which are advanced countries now. Take the United States for example. A hundred and thirty-five years ago, a newspaper named the Pittsburgh Despatch carried an article with the title “What are girls good for?” It said that girls are good mainly for giving birth to children and for keeping house. A girl named Elizabeth, who was 21 years old at that time, did not agree with the article. She wrote a letter to the Editor of the paper arguing that girl

  PHOTO CREDIT: WIKIPEDIA    We had sweets to eat! You may wonder how the new year starts on April 14. Well! This is in Bengaluru and in Chennai, India. People of Tamil origin all over the world follow this practice. Several other states of India observe this day under different names. People from Kerala, the Punjab and Bengal are among those who celebrate New Year’s Day in April. This day used to be the day of the Spring Equinox when the Sun moves from the southern part of the sky to the northern part. For people living in the northern half of the world, this used to mark the beginning of Spring – warmer days and longer hours with sunlight. The Equinox occurs earlier nowadays. In 2023, it was on March 21. However, people stick to the practice of observing April 14 as the new year day. Srinivasan Ramani    

Photo credit: NASA and JPL. Image from Wikimedia Commons.  This image is licensed under the  Creative Commons   Attribution-Share Alike 3.0 Unported  license.  Some of the readers of this blog have been telling me that it is difficult to see Mercury. In Bengaluru, the Sun will rise at about 6:40 AM tomorrow. I have set the alarm to wake me up to see mercury at 6 AM. But it is not always easy for me to get up that early! I have found a good solution to the problem. Tomorrow, the Sun will set in the West, at about 6:30 PM, in Bengaluru. After seven PM, I will be able to see two bright planets in the west. I saw them today. The brighter one is Venus, and it will be lower in the sky than the other. The other one will be Jupiter. I am excited about these planets. More than four hundred years ago, in the year 1610, the Astronomer Galileo started observing these two planets with a home-made telescope. He saw that all of Venus was not uniformly lit. It has phases, like the moon, showing