ABACUS International Math Challenge
for
3rd and 4th graders
February, 2000
A.169. On the same day in the summer of
2000 Sophie is going to be 2000 days old and her father is going to be 2000
weeks old. How old was her father when Sophie was born?
A.170. In the 1*2*3*...*1998*1999=1*9*9*9
equality replace the *'s with + or - signs. Can you do it in such a way
so that the equality is true?
A.171. A king had 7 sons who inherited
all of his castles. He gave his youngest son some castles, the second youngest
got twice as many, the next one got three times as many as the youngest
one, and so on, so the oldest son got 7 times as many as the youngest son.
However, the queen thought that this distribution of the castles was unfair,
so this is what she told her sons: "Every one of you should give 2
castles to every one of your younger brothers, and the youngest one should
just keep everything he receives." This way every son received the
same number of castles. How many castles did the king have?
A.172. Abigail, Bea, Cecilia, and Dori
want to pass through a narrow, dark tunnel. They have a torch that can burn
for 12 minutes. Abigail can make it through the tunnel in one minute, Bea
in two, Cecilia in four, and Dori in five minutes. However, the tunnel is
so narrow that only two of them fit through at a time. They are afraid in
the dark, so they cannot walk in the tunnel without the torch. Can they
all make it through the tunnel?
A.173. Can you write the numbers 0, 1,
2, 3, ..., 8, 9 on the circumference of a circle so that the sum of any
three consecutive numbers is less than 16?
A.174. Can you write the numbers 1, 2,
3, ..., 13, 14 on the circumference of a circle so that the difference of
any two consecutive numbers is either 3, 4 or 5?
A.175. A father had three children, with
all different ages. He distributed among them 9 two-dollar bills and 6 one-dollar
bills. Every child received the same number of bills, and the same amount
of money as his or her own age. How old could the children be?
A.176. There are three finalists in a competition.
The judges asked 10 questions from everybody, and they gave 10 points for
every correct answer, and they took away 5 points for every incorrect answer.
Knowing that the finalist received a total of 240 points, and that the second
competitor had three more correct answers than the first one, find out how
many correct answers each competitor gave.
Please, send your solutions to: