Worksheet Solutions: Number Play

Fill in the Blanks

Q1: In the pattern 3000, 3100, 3200, 3300, ........ 
When placing the number 3600 on a number line, it would be placed just after ________.
Ans: 3500.
Solution: The numbers increase by 100 in each step.

• The sequence is:
  3000, 3100, 3200, 3300, 3400, 3500, 3600, ...
• The number just before 3600 is 3500.

Q2: We are the group of 5-digit numbers between 40,000 and 80,000 such that all of our digits are even. Who is the largest number in our group? Who is the smallest number in our group? 

Ans:
Largest number in the group = 68888
Smallest number in the group = 40000

Q3: In a grid, a supercell is a number that is ________ than its neighbors directly above, below, left, and right.
Ans: larger.
Solution: A supercell is defined as a number that is larger than all of its neighboring numbers in the grid.

Q4: The digit '7' appears ________ times in the tens place from 1 to 100.
Ans: 10.
Solution: The digit '7' appears in the tens place in the numbers 70 to 79, making it appear 10 times.

Q5: On a 12-hour clock, the time 10:10 is interesting because it forms a ________ pattern.
Ans: mirrored.
Solution: The time 10:10 is mirrored because the hour (10) and minute (10) digits are symmetrical, forming a mirror image.

True or False

Q1: The number 2754 would be placed between 2000 and 3000 on a number line.
Ans: True.
Solution: 2754 is greater than 2000 but less than 3000, so it correctly falls between these two values on a number line.

Q2: The number 131 is not a palindrome.
Ans: False.
Solution: 131 is a palindrome because it reads the same forward and backwards.

Q3: On a number line, 9950 would be placed exactly at 10,000.
Ans: False.
Solution: 9950 is slightly less than 10,000, so it would be placed just before 10,000 on a number line.

Q4: The digit '7' appears 100 times in the tens place in numbers from 1 to 1000.
Ans: True.
Solution: The digit '7' appears 100 times in the tens place across the numbers 70-79 in each hundred interval (e.g., 170-179, 270-279, etc.).

Q5: If you reverse the number 123 and add it to the original number, you will get a palindrome.
Ans: True
Solution: Reversing 123 gives 321, and adding them results in 444, which is a palindrome. 

Solve the Following

Q1: Write one 5-digit number and two 3-digit numbers such that their sum is 24,530.

Q2: Pranav uses the digits '5', '2', '6', and '3' to make the smallest and largest 4-digit numbers with them: 2356 and 6532.
The difference between these two numbers is 6532 - 2356 = 4176.
The sum of these two numbers is 8888.

Choose 4-digits to make:

(a) The difference between the largest and smallest numbers greater than 4176.
(b) The sum of the largest and smallest numbers greater than 8888.

Solution: 

(a) Difference greater than 4176

• Digits: 9, 5, 4, and 1
• Largest Number: 9541
• Smallest Number: 1459
• Difference: 9541-1459=8082

8082 > 4176

(b) Sum greater than 8888

• Digits: 9, 7, 6, and 5
• Largest Number: 9765
• Smallest Number: 5679
• Sum:

9765+5679=15444

15444 > 8888

Q3: ​Digit sum 18

(a) Write other numbers whose digits add up to 18.

(b) What is the smallest number whose digit sum is 18?

(c) What is the largest 5-digit number whose digit sum is 18?

(d) How big a number can you form having the digit sum 18? Can you make an even bigger number?

Solution:

(a) Some numbers whose digits add up to 18 are:
99, 189, 198, 279, 288, 369, 378, 459, 468, 549, 558, 639, 648, 729, 738, 819, 828, 909

(b) The smallest number whose digit sum is 18 = 99

(c) The largest 5-digit number whose digit sum is 18 = 99000
(9 + 9 + 0 + 0 + 0 = 18)

(d) We can make very large numbers by keeping most digits as 0, and adjusting just a few digits so that their sum is 18.

For example:

• 900000000000000009 → here the first digit is 9 and the last digit is 9, so the sum is 9 + 9 = 18.
• 99000000000000000000 → here the first two digits are 9 and 9, and the rest are 0s, so the sum is 9 + 9 = 18.

Yes, we can keep adding more and more zeros in between to make the number even bigger.

This shows that there is no largest number with digit sum 18 - we can always make a bigger one.

Q4: Create a 4-digit number where the digit sum is 16, and the number is a palindrome. Provide the number.
Solution: A 4-digit palindrome has the form ABBA, where A and B are digits.

We need to find a palindrome where the sum of the digits is 16, meaning:

A+B+B+A=16

2A+2B=16 

A + B ​=8

Now, A must be a nonzero digit (since it's the first digit of a 4-digit number).

• If A = 1, then B = 7 → Number = 1771
• If A = 2, then B = 6 → Number = 2662
• If A = 3, then B = 5 → Number = 3553

Q5: Identify the numbers marked on the number lines below, and label the remaining positions.

Solution:

Creative and Application-Based Questions

Q1: Mahi is placing numbers on a number line between 1000 and 10,000. She needs to place the number 5030 correctly. Explain where she should place it and why.
Solution: 5030 should be placed just after 5000 on the number line.

• 5030 = 5000 + 30
• This means it is 30 units more than 5000 and still far away from 6000.
• So, on the number line, Mahi should mark 5030 slightly to the right of 5000, close to it.

Q2: Imagine you have a number grid where you want to find a supercell. Describe the steps you would take to identify a supercell in a 3x3 grid.
Solution: Steps to identify a supercell:

1. Look at each number in the grid.
2. Compare it to its neighbors directly above, below, left, and right.
3. If the number is greater than all these neighbors, it is identified as a supercell.
4. Repeat for each number in the grid to identify all supercells.