Problem 16 · 2020 Math Kangaroo
Stretch
Number Theory
place-valuecareful-counting
Marta observed that the number 2020 has the following property: the number formed by the two digits on the left is equal to the number formed by the two digits on the right. How many four-digit numbers, including 2020, have this same property?
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Answer: D — 90
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Hint 1 of 2
The property says the front two digits equal the back two digits.
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Hint 2 of 2
Such a number is just a two-digit block repeated; count the allowed blocks.
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Approach: count the repeated two-digit blocks
- A number with this property looks like the block XY repeated, e.g. 2020 = 20|20.
- The block must be a two-digit number from 10 to 99 (it can’t start with 0).
- That is 90 choices, so there are 90 such numbers.
Mark:
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