ABACUS International Math Challenge
for
7th and 8th graders
September, 2001
C.257. Based on the following views, how
does this building look like?
front view ................................. side view
........................................... top view
C.258. Steve, Frank and John were collecting
cloths, metals, and paper for 3 days. Everybody every day collected at least
1 kg of everything, but Steve, who was the most productive, did not collect
less than 2 kg of anything. Together they collected a total of 86 kg of
material. On the first day they collected 12 kg of paper, 14 kg of metal.
On the second day they collected a total of 44 kg of material. How many
kg of paper did Frank collect on the third day?
C.259. The following numbers are in an
increasing order, where a and b are positive integers. What is the value
of a+b?
C.260. They sell chicken-, duck-, and goose-eggs
on the market. A chicken-egg costs 15 cents, a duck-egg costs 30 cents,
and a goose-egg costs 90 cents. We bought from each kind, a total of 20
eggs for $6. How many of each kind of egg could we buy?
C.261. A father distributed a basket of
plumbs between his sons in the following way: he gave one plumb and 1/9
of the rest of the plumbs to the first son, he gave 2 plumbs and 1/9 of
the rest of the plumbs to the second son, 3 plumbs and 1/9 of the rest of
the plumbs to the third son, and so on. How many sons does he have and how
many plumbs did they each get if everybody got the same amount?
C.262. Place all the digits from 0 to 9
along a circle in any order. Prove that there are 3 consecutively located
digits in any arrangement whose sum is at least 15.
C.263. Using all of the digits 1, 2, 3,
4, and 5, make all the 5-digit numbers. What is their sum?
C.264. The following table shows the results
of the games of an ice hockey league. Every team played every team once.
If Montreal beat Boston 3:0, then what was the final score of the Toronto-Boston
game?
