ABACUS International Math Challenge
for
3rd and 4th graders
January, 2006
A.521. Sandra, Petra and Flora finished
in first, second and third place in a ski race. Next day in school they
said the following to their mutual friend:
Flora: "Sandra did not finish in first place."
Sandra: "Petra did not finish in second place."
Petra: "Flora did not finish in first or third place."
Later they were all laughing and said that only one of them said the
truth. Who finished the race in first and who finished in second place?
A.522. There are 28 students in Franny's
class. 17 of them have skied in Colorado, 13 of them have skied in Switzerland,
and 6 of them have not been in any of these two places How many of them
have skied in both places?
A.523. In a bob race the winner slid down
the 900-meter course in 45 seconds. How many meters could he slide in 1
minute if he could keep this speed?
A.524. There are 8 pairs of black and 7
pairs of red ski gloves in a drawer. (The pairs of gloves are identical
except for their colors.) How many gloves do you have to take out one by
one without looking if for sure you want to have:
a) 1 pair of gloves?
b) 1 pair of black gloves?
c) 2 pairs of gloves?
d) 2 pairs of gloves of different colors?
e) 1 pair of black and 2 pairs of red gloves?
A.525. Hunter Mountain received the first
snow fall. Skiing was OK, but in a week half of the snow melted. However,
the following week twice as much snow fell as the first time and this way
45 cm of snow covered the mountain. How many cm of snow fell the first time?
A.526. In a snowman making competition
the children made 60 snowmen. The heads of the snowmen followed a particular
pattern shown on the diagram below. How do the heads of the 10th, the 25th
and the 60th snowmen look like?
A.527. There are 7 ski lifts on the slopes
of White Cap Mountain. From the base 4 lifts are taking the skiers to the
middle of the trails, out of which at least 3 lifts are working on any given
day. They built 3 lifts from the middle of the mountain to the top, out
of which only two are working on any given day. How many different ways
can they operate the lifts?
A.528. The children are preparing for a
snowball fight. They prepared their ammunition (i.e. snowballs) and put
them in four 5-layer pyramids. The first layer on the ground in each pyramid
is square shaped, and the 5th layer is just one snowball. In a new layer
they always put a snowball on top of 4 snowballs in the lower layer. How
many snowballs could they possible make?
Please, send your solutions to: