E.1.1. Without any repetition, form the highest possible number and smallest possible number of four digits using the digits given below.
a) 2, 8, 7, 4
b) 9, 7, 4, 1
c) 4, 7, 5, 0
d) 1, 7, 6, 2
e) 5, 4, 0, 2
(Hint: 0754 is a three digit number)
Solution:
To form the highest possible number:
a) 8 7 4 2
b) 9 7 4 1
c) 7 5 4 0
d) 7 6 2 1
e) 5 4 2 0
To form the smallest possible number:
a) 2 4 7 8
b) 1 4 7 9
c) 4 0 5 7
d) 1 2 6 7
e) 2 0 4 5
E.1.2. Form the highest and smallest number using any of the digits twice.
a) 3, 8, 7
b) 9, 0, 5
c) 0, 4, 9
d) 8, 5, 1
(Hint: Think about all the terms about using a digit twice)
Solution:
To form the highest and smallest numbers using any of the digits twice,
a) 3, 8, 7
Highest: 887
Smallest: 337
b) 9, 0, 5
Highest: 995
Smallest: 509
c) 0, 4, 9
Highest: 990
Smallest: 409
d) 8, 5, 1
Highest: 885
Smallest: 115
These are the highest and smallest numbers that can be formed using each set of digits with one digit repeated.
E.1.3. Form the highest and smallest possible numbers by using four different digits given below and by fulfilling all the terms stated below. (The first one is solved for you)
a) Digit 7 has to be in the place of Ones.
(The number must not begin with 0. Why?)
b) Digit 4 has to be in place of Tens.
c) Digit 9 has to be in place of Hundreds.
d) Digit 1 has to be in place of Thousands.
Solution:
Let's find the highest and smallest possible numbers using the given digits while fulfilling the conditions:
a) Digit 7 has to be in the place of Ones.
Largest: 9 8 6 7
Smallest: 1 0 2 7
These numbers fulfill the given conditions, ensuring that the number must not begin with 0 to maintain it as a four-digit number.
b) Digit 4 has to be in place of Tens.
Largest: 9 8 4 7
Smallest: 1 0 4 2
c) Digit 9 has to be in place of Hundreds.
Largest: 8 9 7 4
Smallest: 1 9 0 4
d) Digit 1 has to be in place of Thousands.
Largest: 1 9 8 7
Smallest: 1 7 8 9
These numbers fulfill the given conditions, and none of them begins with 0, maintaining them as four-digit numbers.
E.1.4. a) Express the number 5789654238745 in the local and international system.
b) How do we write numbers above crore in the local and international system?
Solution:
Answer will be posted soon. Please wait...
E.1.5. Solve the puzzle
There is a birthday gift for you in the box below. But the problem is the box is locked. Just below the lock the digits from 0 to 9 are written. For opening the lock you need a secret three digit number. Different features of that secret number are mentioned in the paper below.
Now, find out the secret number and win gifts.
Solution:
Based on the clues provided:
From "6 8 2", one digit is correct and in the right place. This means the secret number contains a "2" in the third position.
From "6 1 4", one digit is correct but in the wrong place. This means the secret number contains a "6", but not in the first position.
From "2 0 6", two digits are correct and in the right place. This confirms that "2" is in the third position and "0" is in the second position.
From "7 3 8", none of the digits are correct. This means the secret number does not contain 7, 3, or 8.
From "7 8 0", one digit is correct but in the wrong place. This means the secret number contains an "8" but not in the second position.
Considering these clues, the secret number is "0 6 2".
E.1.6. Write the name of a friend. The name must have less than 9 letters. Now do the following:
Tell your teacher the number in the green box. Your teacher will tell you your age. Show this magic trick to your friend, family members, relatives and neighbours. What happens if the number of letters of your friend’s name is more than 9?
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