ABACUS International Math Challenge
for
5th and 6th graders
November, 2002
B.337. I have four analog clocks. One of
them is 2 minutes fast every hour, another one is 3 minutes late every hour,
the third one is always on time, and the fourth clock does not work. One
day in the daytime I set the three working clocks to show the exact time
at that same moment, but in the evening of the same day at one point the
four clocks showed the following times: 5 minutes to 11 o'clock, 10 minutes
after 11 o'clock, 25 minutes after 11 o'clock, and quarter to 12 o'clock.
What time did I set the clocks?
B.338. Color the following diagram so that
any two neighboring fields are different colors. How many colors do you
need the least?
B.339. Peter's grandmother was born in
the year abcd. If she were still alive she would have turned ab
+ cd years old in 2002. Which year was she born? (abcd is
a number created from the digits a, b, c, and d.)
B.340. A man figured out that he can cover
the floor of a square-shaped room with tiles without having have to cut
any tile. First he put tiles all around the edges of the floor using 56
tiles. How many tiles does he need to cover the whole floor?
B.341. The sum of three positive whole
numbers is 2002. Out of these three numbers the greatest one is 337 greater
than the one in the middle, which is 330 more than the smallest number.
What are these three numbers?
B.342. Using all 10 digits exactly once,
write down 5 two-digit numbers so that the smallest number is a divisor
of all the other numbers.
B.343. Every edge of a cube is colored
to either black or red so that there is at least one black edge on every
side of the cube. At least how many black edges are there on the cube?
B.344. A prisoner received the map below
about the roads that may take him outside of the prison. (Wherever the road
splits, the prisoner may go left or right, but he may not turn back.) The
roads lead to 4 doors. When he opens a door, he will either be free, or
hungry lions will be waiting for him. There are hungry lions at the end
of 3/4 of all the possible ways. Which door should he go to so that he could
be free?
prisoner
Please, send your solutions to: