Why is the Collatz conjecture correct for all the starting numbers in the sequence of powers of 2?
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1 Marks Question
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2 Q→05Case study (4 Marks)
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Check if the Collatz conjecture holds for the starting number 100.
Construct Collatz sequence starting with your favourate whole number. Do you always reach 1.
Will reversing and adding numbers repeatedly, starting with a 3-digit number, always give a palindrome?
Will reversing and adding numbers repeatedly, starting with a 2 -digit number, always give a palindrome?.
Make the Collatz sequence beginning with 17.
Construct the Collatz sequence starting with 22.
How many rounds (iterations) does your year of birth take to reach the Kaprekar constant?
Apply Kaprekar's routine on a two-digit number. What number will start repeating?
What is the sum of the smallest and the largest 6-digit palindromes?
Label the remaining positions by observing the patterns of numbers on the number line below:
Calculate the digit sums of
(i) 4-digit numbers
(ii) 5-digit numbers
whose digits are consecutive. Do you notice any pattern?
(i) 4-digit numbers
(ii) 5-digit numbers
whose digits are consecutive. Do you notice any pattern?
Write two five digit numbers whose sum is 28,500.
Form the largest and smallest 4-digit numbers using each of digits 7, 1, 0, 5 only once.
In a four digit number, the digit in one's place is 3 times the digit in the ten's place, The digit in hundred's place is 5 times that in ten's place. The thousand's place digit is 6 more the digit in the ten's place.
In the following figure numbers are written in the boxes in three columns. Arrows are directed towards the first and third columns from the boxes in the second column. The number in the box in first or third column is sum of the numbers in the middle row from which arrows originate.
For example,
$\begin{array}{l}3,400=1,500+1,500+400 \\ 38,800=25,000+400+400+13,000\end{array}$
Similarly, draw arrows from the boxes in the middle column to the numbers on the side columns to obtain the following sums: $14,000,\ 25,000,\ 16,000$
Can we make 1,000 using the numbers in the middle column?
View full solution →For example,
$\begin{array}{l}3,400=1,500+1,500+400 \\ 38,800=25,000+400+400+13,000\end{array}$
Similarly, draw arrows from the boxes in the middle column to the numbers on the side columns to obtain the following sums: $14,000,\ 25,000,\ 16,000$
Can we make 1,000 using the numbers in the middle column?
Consider the numbers in the following boxes:
Using these numbers and the operations addition and subtraction, we can write: $39,800=40,000-800+300+300$
Similarly, write the following numbers by using the numbers in the boxes:
$45,000 ; 5,900 ; 17,500 ; 21,400$
View full solution →Using these numbers and the operations addition and subtraction, we can write: $39,800=40,000-800+300+300$
Similarly, write the following numbers by using the numbers in the boxes:
$45,000 ; 5,900 ; 17,500 ; 21,400$
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