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Algebra Play

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Page 135: 1. Think of a number. 2. Double it. 3. Add four. 4. Divide by two. 5. Subtract the original number you thought of. I…
Page 136: How would you change this game to make the final answer 3? What about 5?
Page 136: Can you come up with more complicated steps that always lead to the same final value?
Page 136: 1. Think of a date. (Mukta thinks of 26/01, Republic Day, but doesn't say it aloud.) 2. Multiply the month by 5. (1…
Page 137: Mukta thinks of another date, follows the same steps, and reports her answer as 1390. What date did Mukta start with…
Page 137: Find the dates if the final answers are the following: (i) 1269 (ii) 394 (iii) 296 You can try this trick with your…
Page 137: Can you change the steps in this trick and still find the original date? Instead of subtracting 165 from the final…
Page 137: Try to devise your own 'Think of a Number' trick.
Page 137: In a number pyramid, each number is the sum of the two numbers directly below it.
Page 138: Use the same rule to fill these pyramids:
Page 138: How do we fill this pyramid?
Page 138: What about filling in the numbers in this pyramid? Where do we start?
Page 139: Let us fill the empty boxes with letter-numbers.
Page 139: Fill the following pyramids:
Page 139: What is the relationship between the numbers in the bottom row and the number at the top? Let us start with the…
Page 140: What about a pyramid with three rows? Using letter numbers for the bottom row, we can write an expression for the…
Page 140: Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases.
Page 140: Write an expression for the topmost row of a pyramid with 4 rows in terms of the values in the bottom row.
Page 140: Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases.
Page 140: If the first three Virahānka-Fibonacci numbers are written in the bottom row of a number pyramid with three rows,…
Page 140: What can you say about the numbers in the pyramid and the number at the top in the following cases? (i) The first…
Page 140: If the bottom row of an n row pyramid contains the first n Virahānka-Fibonacci numbers, what can we say about the…
Page 141: Can we find the 4 numbers in the grid from just knowing this sum?
Page 141: Suppose you are told that the sum is 36. Can you find the 4 numbers in the grid?
Page 142: Create your own calendar trick. For instance, choose a grid of a different size and shape.
Page 142: In this grid, shapes represent numbers. How do we find the value of each shape?
Page 142: In the following grids, find the values of the shapes and fill in the empty squares:
Page 142: Fill the digits 2, 3, and 5 in [ ][ ] × [ ], using each digit once. What is the largest product possible?
Page 143: How do we find the largest product among these six options, without just computing all of them?
Page 143: In this case, we used the largest digit as the multiplier. The other two digits were arranged in decreasing order to…
Page 144: Fill the digits 1, 3, and 7 in [ ][ ] × [ ] to make the largest product possible.
Page 144: Fill the digits 3, 5, and 9 in [ ][ ] × [ ] to make the largest product possible.
Page 144: 1. Choose a 2-digit number of different digits and don't reveal it! (Shubham picks 47.) 2. Reverse the digits to get…
Page 145: If b > a, then ba > ab. So, the difference is (10b+a) − (10a+b) = 10b − b − 10a + a = 9b − 9a = 9(b−a). The…
Page 145: In the trick given above, what is the quotient when you divide by 9? Is there a relationship between the two numbers…
Page 145: In the trick given above, instead of finding the difference of the two 2-digit numbers, find their sum. What will…
Page 145: Consider any 3-digit number, say abc (100a+10b+c). Make two other 3-digit numbers from these digits by cycling these…
Page 145: Consider any 3-digit number, say abc. Make it a 6-digit number by repeating the digits, that is abcabc. Divide this…
Page 145: The magical pond problem: 3 shrines, each with a doubling pond, equal flowers placed at each.
Page 146: A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs is…
Page 146: A mother is 5 times her daughter's age. In 6 years' time, the mother will be 3 times her daughter's age. How old is…
Page 146: Two friends, Gauri and Naina, are cowherds. One day, they pass each other on the road with their cows. Gauri says to…
Page 146: (i) If I sell 100 dosas a day, what should be the selling price of my dosa to make a profit of ₹2000? (ii) If my…
Page 146: Evaluate the following sequence of fractions: What do you observe? Can you explain why this happens?
Page 147: (i) How many coins did Karim initially have? (ii) For what cost per round should Karim agree to the deal, if he…

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