Question

What is the number of whole numbers
formed on the screen of a calculator
which can be recognised as numbers
with (unique) correct digits when they are
read inverted? The greatest number that
can be formed on the screen of the
calculator is 999999.​

Answer 1

The digits which can be recognised as unique digits when they are Inverted in a calculator are 0, 1, 2, 5, 6, and 9 Since the number cannot begin with zero all the numbers having 0 at units place should be discarded for otherwise when reed upside down the number yen begin with 3 we now :1St the different posibililities

1

7

2

6

×

6

=

6

2

6×6=62

3

6

×

7

×

6

=

6

2

×

7

6×7×6=62×7

4

6

×

7

×

7

×

6

=

6

2

×

7

2

6×7×7×6=62×72

5

6

×

7

×

7

×

7

×

6

=

6

2

×

7

3

6×7×7×7×6=62×73

6

6

×

7

×

7

×

7

×

7

×

6

=

6

2

×

7

4

6×7×7×7×7×6=62×74

Thus, the number of required numbers

=

7

+

6

2

+

6

2

×

7

+

…

+

6

2

×

7

4

=7+62+62×7+…+62×74

=

7

+

6

2

(

7

3

−

1

)

7

−

1

=

7

+

6

(

7

5

−

1

)

=

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