ABACUS International Math Challenge
for
7th and 8th graders
December, 1999
C.153. 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?
C.154. Could the sum of seven consecutive
whole numbers be a prime number?
C.155. 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.
C.156. 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.
C.157. 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?
C.158. 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?
C.159. 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?
C.160. Find a, b, c, and d, such that 
.
Please, send your solutions to: