Do you think you are SMART?
Prove by Solving this Puzzle!
By: Mukul Sharma
Mukul Sharma is a multifaceted personality, having acted in films, run a pest control business, made TV serials, partnered an ad agency, produced front page pocket cartoons for The Telegraph newspaper and edited Science Today magazine for six years. He has written Dream Sequence, an anthology of science fiction short stories, among other works. He is a member of International Science Writers Association. He also has to his credit a weekly spiritual column for the Economic Times. But that's not why we are introducing him in these pages. He has been running a popular puzzle column Mindsport in a leading daily for many years now. Starting this issue, we bring to you a puzzle by Mukul Sharma every month. Pull up your socks for the mental jog
Puzzle of the Month
Take a three-by-three square grid, which has the number ‘1’ already inserted in the third row, middle square. You have to complete it by putting eight different prime numbers in the remaining eight empty squares so that the rows, columns and diagonals add up to the same total and it must be the smallest possible total under the conditions. To help you, the number in the middle square is the average of the two numbers directly above and below it and the third largest number is not in the right-hand column. Every square contains one or two digits.
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Answer will be published in the July issue
Last Puzzle and the Answer
Take any set of numbers from any category, anywhere, such as the lengths of different rivers of the world, the day’s stock quotations, numbers appearing on the newspaper front page, city populations, molecular weights of compounds, half-lives of radioactive atoms -- anything in fact with no connection with one another. What’s the chance that any particular number (not zero though) will be the first digit? One would imagine it should be one chance in nine for any number, 1 to 9, right? Wrong. According to a particular law (not named here to prevent you from googling it!), the chances of number 1 coming in the first place is much higher than, say, number 9. The actual percentage breakdown for numbers from 1 through 9 is: 30.1%, 17.6%, 12.5%, 9.7%, 7.9%, 6.7%, 5.8%, 5.1%, 4.6%. Why does this happen?
Answer:
It is called the Benford’s Law and it works like this: Imagine all the integers in a line. This will have 1-digit numbers starting with 1, 2, 3 . . . 8, 9; then 2-digit numbers starting with 1, 2, 3 . . . 8, 9 and so on. Now the number of ‘x’ digit numbers starting with a particular digit in a row will be 10^(x - 1). One thing we observe in this line is that the gap (i.e., number of ‘x’ digit numbers and ‘x + 1’ digit numbers) lying between run of ‘x’ digit numbers and ‘x + 1’ digit numbers of that particular digit is much less for a lower digit than for a higher one. Hence, the chances for a hit are greater.
For the gap ‘g’ between the ‘x’ digit run and ‘x + 1’ digit run for a digit ‘a’, we have the formula
g = (9 - a)*(10^X) + (a - 1)*(10^X + 1). Hence, the bigger the gap, the lesser will be the chance for a hit.
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