e-Numbers
Maths Olympiad Problems | Maths Contest Problems | PRMO Questions | NSEJS Maths Questions
Important for ---- NTSE Stage 2, Maths Olympiads, PRMO, RMO, INMO
The digits on many electronic devices look like this:
When numbers made of these digits are rotated 180◦ ( CW ), some of them become numbers and some don’t. For example, when 8 is rotated it remains the same, 125 becomes 521, and 14 does not become a number. Except for 0, no number starts with 0
All rotations referred to below are through 180◦.
a) List all digits which rotate to the same digit.
b) List all digits which rotate to a different digit.
c ) List all numbers from 10 to 50 whose rotations are numbers.
d) List all numbers from 50 to 200 that stay the same when rotated.
Answers:a) The digits which rotate to the same digit are: 0, 1, 2, 5, 8.
b) The digits which rotate to a different digit are 6 and 9.
c) Only the digits in Parts a and b can be used to form numbers whose rotations are numbers. So the only numbers from 10 to 50 whose rotations are numbers are: 11, 12, 15, 16, 18, 19, 21, 22, 25, 26, 28, 29.
d) From Parts a and b, if a number and its rotation are the same, then the first and last digits of the number must both be 1, 2, 5, 8, or the first digit is 6 and the last 9 or the first 9 and the last 6. So the numbers from 50 to 200 that stay the same when rotated are: 55, 69, 88, 96, 101, 111, 121, 151, 181.
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