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What is the greatest palindrome between 1 and 1000 whose digits add up to 15?
717
What is the predecessor of the smallest 4 digit number?
Predecessor of a number is obtained by subtracting 1 from it. The smallest 4 digit number is 1000 and its predecessor is 1000 - 1 = 999.
Which prime number between 1 and 100 is a palindrome?
only 1, 11
The smallest non-palindromic number whose square is a palindrome?
That would be 26 . . . its square is 676.There are two smaller palindromic squares . . . 121 and 484 ... but they're the squares of11 and 22 respectively, which are palindromic, so they flunk the question's specifications.
What is the difference between the smallest perfect square larger than 1 million and the largest perfect square smaller than 1 million?
1 million = 1,000,000 = 1000² Which means we want: (1000 + 1)² - (1000 - 1)² , that is 1001² - 999² However, before we work that out, lets look at what we have. let a = 1000, b = 1, then: (1000 + 1)² - (1000 - 1)² = (a + b)² - (a - b)² Now (a + b)² = a² +2ab + b² and (a - b)² = a² - 2ab - b² → (a + b)² - (a - b)² = a² +2ab + b² - (a² - 2ab - b²) = 4ab As a = 1000, b = 1, this means (1000 + 1)² - (1000 -1)² = 4 × 1000 × 1 = 4000.
