Question 3
Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
FIO-3
Chapter: NUMBER PLAY
Class: 6 (Class 6)
Category: figure_it_out
Question
Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
Question diagram(s):
We must find the rule for "supercells" from the example.
Step 1 — Finding the Supercell Rule
We look at the supercells: 999, 555, 666, 498, 501. We look at the non-supercells: 101, 444, 298, 397. We check for divisibility by 3. We add up the digits of each number. If the sum divides by 3, the number divides by 3.
For supercells: 27 divides by 3. 15 divides by 3. 18 divides by 3. 21 divides by 3. 6 divides by 3. All supercells divide by 3.
For non-supercells: 2 does not divide by 3. 12 divides by 3. 19 does not divide by 3. 19 does not divide by 3.
All supercells divide by 3. Most non-supercells do not divide by 3. But 444 divides by 3. Yet 444 is not a supercell. So, a supercell divides by 3. It is also not the number 444. Numbers must be between 100 and 999.
Step 2 — Filling the Table and Identifying Supercells
We will fill the table with the given numbers. The numbers are: 999, 101, 555, 444, 666, 298, 498, 397, 501. Now we check each number using our supercell rule.
For 999: Sum of digits is 27. 27 is divisible by 3. It is not 444. So, 999 is a supercell.
For 101: Sum of digits is 2. 2 is not divisible by 3. So, 101 is not a supercell.
For 555: Sum of digits is 15. 15 is divisible by 3. It is not 444. So, 555 is a supercell.
For 444: Sum of digits is 12. 12 is divisible by 3. It IS 444. So, 444 is not a supercell.
For 666: Sum of digits is 18. 18 is divisible by 3. It is not 444. So, 666 is a supercell.
For 298: Sum of digits is 19. 19 is not divisible by 3. So, 298 is not a supercell.
For 498: Sum of digits is 21. 21 is divisible by 3. It is not 444. So, 498 is a supercell.
For 397: Sum of digits is 19. 19 is not divisible by 3. So, 397 is not a supercell.
For 501: Sum of digits is 6. 6 is divisible by 3. It is not 444. So, 501 is a supercell.
We have found 5 supercells in the table. The supercells are 999, 555, 666, 498, and 501.
Answer
(i) The filled table is: [999, 101, 555, 444, 666, 298, 498, 397, 501]. (ii) The supercells are: 999, 555, 666, 498, 501. (iii) There are 5 supercells in this table.
More questions in FIO
Colour or mark the supercells in the table below.
Fill the table below with only 4-digit numbers such that the supercells are exactly the coloured cells.
Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
Out of the 9 numbers, how many supercells are there in the table above?
Find out how many supercells are possible for different numbers of cells.
Do you notice any pattern? What is the method to fill a given table to get the maximum number of supercells? Explore and share your strategy.
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 why not?
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 supercell. Is it possible?
Make other variations of this puzzle and challenge your classmates.
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 the largest number in each of the sequences above.
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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?
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a. the difference between the largest and smallest numbers greater than .
b. the difference between the largest and smallest numbers less than .
c. the sum of the largest and smallest numbers greater than .
d. the sum of the largest and smallest numbers less than .
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?
Write an example for each of the scenarios shown in the diagram whenever possible.
Always, Sometimes, Never?
Below are some statements. Think, explore and find out if each of the statement is 'Always true', 'Only sometimes true' or 'Never true'. Why do you think so? Write your reasoning and discuss this with the class.
a. 5-digit number + 5-digit number gives a 5-digit number
b. 4-digit number + 2-digit number gives a 4-digit number
c. 4-digit number + 2-digit number gives a 6-digit number
d. 5-digit number – 5-digit number gives a 5-digit number
e. 5-digit number – 2-digit number gives a 3-digit number
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 classroom door to the school gate d. From your school to your home
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
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Estimate the number of holidays you get in a year including weekends, festivals and vacation. Then, try to get an exact number and see how close your estimate is.
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 their 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?