ABACUS - JANUARY 2012 : LEVEL 7 - 8
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Muhammad Yusuf
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PROBLEM 1. The
ages of a father and his two different-aged sons are the powers of the same
prime number. Last year everybody's age was a prime number. How old are they
now?
PROBLEM 2. Could
the sum of seven consecutive integers be a prime number?
PROBLEM 3. A
5-digit number is divisible by 7, 8, and 9. The number created from the first
two digits is a prime number, 1 greater than a square number, and the sum of
these two digits is a two-digit number. Find this 5-digit number.
PROBLEM 4. Every
digit of a 5-digit number is either 1 or a prime number. Not only that, but any
number created by any 2, 3, or 4 consecutive digits of this number are prime
numbers also. Find this number, and check if it is a prime number or not.
PROBLEM 5. Can
you put the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 into two groups so that
the sums of the numbers in each group is the same? Can you do this to get the
same product in each group?
PROBLEM 6. Are
there any five consecutive whole numbers, which can be put into two groups so
that the product of the numbers in each group is the same?
PROBLEM 7. In
some cases, when 22022 and 20222 are divided by the same 3-digit number, they
give the same remainder. Which one of these divisors can be determined by the
remainder?
PROBLEM 8. Find
a, b, c, and d, such that abb
= bccbdc
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