42 solutions available
Fill the table below with only 4-digit numbers such that the supercells are exactly the coloured cells.
Out of the 9 numbers, how many supercells are there in the table above? _____________
For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible?
Can you fill a supercell table without repeating numbers such that there are no supercells? Why or why not?
Will the cell having the largest number in a table always be a supercell? Can the cell having the smallest number in a table be a supercell? Why or...
Fill a table such that the cell having the second largest number is not a supercell.
Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a super cell. Is it possible?
Make other variations of this puzzle and challenge your classmates.
Complete Table 2 with 5-digit numbers whose digits are ‘1’, ‘0’, ‘6’. ‘3’, and ‘9’ in some order. Only a coloured cell should have a number greater...
Identify the numbers marked on the number lines below, and label the remaining positions. Put a circle around the smallest number and a box around...
Find out how many numbers have two digits, three digits, four digits, and five digits:
Digit sum 14 (a) Write other numbers whose digits add up to 14. (b) What is the smallest number whose digit sum is 14? (c) What is the largest...
Find out the digit sums of all the numbers from 40 to 70. Share your observations with the class.
Calculate the digit sums of 3-digit numbers whose digits are consecutive (for example, 345). Do you see a pattern? Will this pattern continue?
Among the numbers 1-100, how many times will the digit ‘7’ occur? Among the numbers 1-1000, how many times will the digit ‘7’ occur?
Write all possible 3-digit palindromes using these digits.
Puzzle time I am a 5-digit palindrome. I am an odd number. My ‘t’ digit is double of my ‘u’ digit. My ‘h’ digit is double of my ‘t’ digit. Who am I?...
Try and find out all possible times on a 12-hour clock of each of these types.
Find some other dates of this form from the past.
Find all possible dates of this form from the past.
But, will any year’s calendar repeat again after some years? Will all dates and days in a year match exactly with that of another year?
Pratibha uses the digits ‘4‘7’, ‘3’and ‘2’ and makes the smallest and largest 4-digit numbers with them: 2347 and 7432. The difference between these...
What is the sum of the smallest and largest 5-digit palindrome? What is their difference?
The time now is 10:01. How many minutes until the clock shows the next palindromic time? What about the one after that?
How many rounds does the number 5683 take to reach the Kaprekar constant?
Can we make 1,000 using the numbers in the middle? Why not? What about 14,000, 15,000 and 16,000? Yes, it is possible. Explore how. What thousands...
Always, Sometimes, Never? Below are some statements. Think, explore, and find out if each of the statements is ‘Always true’, ‘Only sometimes true’,...
Share and discuss in class the different methods each of you used to solve these questions.
Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1?
Steps you would take to walk (a) From the place you are sitting to the classroom door (b) Across the school ground from start to end (c) From your...
Number of times you blink your eyes or number of breaths you take: (a) In a minute (b) In an hour (c) In a day
Name some objects around you that are: (a) a few thousand in number (b) more than ten thousand in number
There is only one supercell (number greater than all its neighbours) in this grid. If you exchange two digits of one of the numbers, there will be 4...
How many rounds does your year of birth take to reacall the Kaprekar constant?
We are the group of 5-digit numbers between 35,000 and 75,000 such that all of our digits are odd. Who is the largest number in our group? Who is the...
Estimate the number of holidays you get in a year including weekends, festivals, and vacations. Then try to get an exact number and see how close...
Estimate the number of liters a mug, a bucket, and an overhead tank can hold.
Write one 5-digit number and two 3-digit numbers such that theif sum is 18,670.
Choose a number between 210 and 390. Create a number pattern similar to those shown in Section 3.9 that will sum up to this number.
Recall the sequence of powers of 2 from chapter 1, table 1. Why is the Collatz conjecture correct for all the starting numbers in this sequence?
Check if the Collatz Conjecture holds for the starting number 100.
Starting with 0, players alternate adding numbers between 1 and 3. The first person to reach 22 wins. What is the winning strategy now?
