ABACUS International Math Challenge
for
7th and 8th graders
January, 2002
C.289. Sarah mama wants to bake 4 meatballs,
but only three of them fit in her pan at a time. It takes 5 minutes to bake
one side of a meatball, and 5 minutes to bake the other side. Without cutting
the meatballs, can all 4 of them be baked in less than 20 minutes?
C.290. A few tractors plow a 300-acre land
in a whole number of days. Every tractor plows 15 acres every day. How many
more tractors could finish the job 6 days earlier?
C.291. Herbert has 10 three-armed candle
holders. He wants to buy candles for them so that all three candles of every
candle holder would be either the same color or all three candles would
be different colors. He walks in a candle shop that has a total of 70 candles
for sale. Prove that he can buy all the candles he needs here.
C.292. Find a 4-digit square number in
which the first two and the last two digits are the same.
C.293. We grouped the odd numbers in the
following way: (1); (3, 5); (7, 9, 11); (13, 15, 17, 19); ... What is the
sum of the numbers in the 100th group?
C.294. The archeologists are working on
an excavation site of a Roman marketplace. They know that the marketplace
is square shaped, was surrounded by 4 walls, there was a well in the middle
of the marketplace in which the merchants poured their gold in case of a
barbarian attack. In two opposite corners of the market place stood the
statues of Jupiter and Juno. The archeologists found the statue of Juno
and the corner of the marketplace marked by a 1 meter long section of both
walls running from this corner behind Juno, and a marking pole (showing
the different directions towards the two statues) that was placed outside
of the walls. How can the archeologists locate the well with all the gold
in it?
C.295. In Chocolate Land they produce sheets
of chocolate with 30 little squares in a 5x6 arrangement. Pete wants to
cut up the sheet with a sharp knife into 30 little squares. How many cuts
does he need the least if he may rearrange the pieces the way he wants to
after every cut?
C.296. Every spring a Chinese family consumes
90 heads of a delicious lattice. This lattice propagates from seeds. Every
lattice brings 10 seeds, but when it has seeds its leaves turn bitter and
you cannot eat them. How many seeds does this family need if they want to
produce enough lattice to eat and enough seeds for next year?