The problems are not in any specific order.
Some problems are just harder that other problems here.
scroll down for solutions
1. a natural number n can be replaced by ab if a + b = n
is it possible, if we start with n=22 to get to 2001??
prove.
(turgor 2005)
2.What is the unit digit of the sum 1! + 2! + 3! +...+15!?
(mathcounts 1985)
3.palindromes, like 23432, read the same forward and backwards.
Find the sum of all four-digit positive integer palindromes.
(mandelbrot #3)
4. Find the greatest n for which
12n. evenly divides by 20!.
(mandelbrot #1)
5.How many factors of
295. are there which are greater than 1,000,000?
(mathcounts 1984)
6. if n=100, find the value of (n+1)!/(n-1)!.
(mathcounts 1988)
7. If
9n2. -30n + c is a perfect square for all integers n,what is the value of c?
8.what is the largest base 10 number that can be expressed as a 3-digit base 5 number?
(mathcounts 1989)
Solutions
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