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Page 26 - Math Genius C2
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    E:\Working\Orange_Education\Math_Genius_2\Open_Files\Chap_01
                   \ 26-Sep-2025  Bharat Arora   Proof-10                                   Reader’s Sign _______________________ Date __________

                  example: Arrange the numbers 250, 168, 900, 525 in descending order.

                  Solution: All the given numbers have 3 digits. So, we compare the digits                      H T O

                               in the hundreds place first.                                                     2 5 0

                               We see that 9 > 5 > 2 > 1                                                        1 6 8
                               So, the descending order of the numbers is:                                      9 0 0

                               900 > 525 > 250 > 168                                                            5 2 5

                  FORMatION OF tHE GREatESt aND SMaLLESt 3-DIGIt NUMBERS

                  Let us form numbers with 3, 8 and 6 using each digit exactly once.
                                                                                           H T O          H T O
                  Keeping 3 in the hundreds place, we have two numbers  3 6 8  and  3 8 6.

                  Keeping 6 in the hundreds place, we have two numbers  6 3 8  and  6 8 3.

                  Keeping 8 in the hundreds place, we have two numbers  8 3 6  and  8 6 3.

                  Among the six numbers so formed, 368 is the smallest and 863 is the greatest number.

                  If we take a close look at these numbers, we see that                            Be Aware
                  368 has the digits in ascending order and 863 has the                      Zero is not used in the first

                  digits in descending order.                                                place of a 3-digit number. It
                                                                                             can be used in the second
                  Thus, we can say:                                                          place, for example, with 5,
                  •  To form the greatest number, we arrange the given                       8, and 0, the smallest 3-digit
                                                                                             number is 508. 058 is not
                      digits in descending order.                                            correct, as it is read as 58.

                  •  To form the smallest number, we arrange the given                       We can make 6 different

                      digits in ascending order.                                             3-digit numbers using any 3
                                                                                             different digits (except 0),
                  example: Write all the 3-digit numbers that contain the                    without repeating them.

                  digits 7, 2 and 5. Also, find the smallest and the greatest

                  number among these numbers and write their number names.
                  Solution: 3-digit numbers that contain 7, 2 and 5 are: 725, 752, 527, 572, 257, 275.

                               Smallest number: 257               Two hundred fifty-seven

                               Greatest number: 752               Seven hundred fifty-two

                                                              Math Insight
                       987 is the greatest 3-digit number which has three distinct digits, and 102 is the smallest
                       3-digit number which has three distinct digits.

                  24                                                                                    Mathematics-2

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