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Earn +20 ptsQ: How many two digit numbers have digits whose sum is a perfect square?
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How many 2 digits numbers are such that the difference of the number and the number with the digits reversed is a perfect square?
If the number with the digits reversed can have a leading 0 so that it is a 1-digit number, then 16. Otherwise 13.
How many 5-digit integers are perfect squares?
The smallest 5-digit integer perfect square is 10,000 = (100)2The largest 5-digit integer perfect square is 99,856 = (316)2So we want to know how many numbers that is, from 100 to 316 inclusive.It's 316 minus the first 99 = 217 of them.
What is the probability that a randomly selected two-digit positive integer is a perfect square or a perfect cube?
There are 90 two-digit numbers from 10 to 99. Of those, 6 are perfect squares (16, 25, 36, 49, 64, and 81) and 2 are perfect cubes (27 and 64). Each perfect square or root has a probability of 1 in 90 in being drawn.
How many three digit numbers are there such whose digits sum is odd?
450.
The largest three digit perfect square?
961 961
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