5th and 6th graders
March 2015
B.1017. Steve, Alex, Leslie, and Kate each have a favorite car, a favorite type of chocolate, and they each have a dog. We have the following information about them:
- The owner of Bell loves chocolate with almond.
- Alex is dreaming of a Honda while he is eating milk chocolate.
- Kate takes Caesar for a walk every Sunday.
- The owner of Trixie would love to have a Jaguar.
- Leslie never buys anything but chocolate with yogurt.
What is the name of the owner of Fletcher? Who loves chocolate with raspberry?
B.1018. See the balance on the following diagram, which shows that every arm of the balance is in equilibrium. (The horizontal bars are suspended at their midpoints.) Identical shapes have identical masses. The mass of the square is 1 dkg. What are the masses of the other shapes?
B.1019. Two cities (A and B) are connected by a straight road. There are 5 other cities on this road between cities A and B. The distance between any two out of these 7 cities is a whole number of kilometers. If somebody walks from one city to another, from the number of kilometers walked you can tell exactly between which two cities the person walked. City A is 25 km from City B. Give a possible arrangement for the locations of the 5 other cities between A and B.
B.1020. Look at the following interesting two pairs of products: 12x42 = 21x24; 21x48 = 12x84. As you can see, when you switch the digits of the 2-digit factors, you get two new factors but the product does not change. Give at least three more similar interesting products.(You will get 5 points for 3 interesting products, and one bonus point for each 3 additional products.)
B.1021. A 5 cm long snail wanted to climb out of a dry well using the vertical walls of the well. The snail was rested and climbed up 10 bodylengths in the first minute, 9 bodylengths in the second minute, and so on. After the 10th minute the snail stops to rest for awhile. After resting a little, it continues to climb the same way as before. The snail started at the bottom of the well, but half way up it slipped and slid back down to one quarter of the whole depth. Here it rested again and then after 10 minutes of climbing the same way, it was still only at 2/3 of the way up. How deep it this well?
B.1022. A 5-digit number E rounded to the nearest tenthousands is A, rounded to the nearest thousands is B, rounded to the nearest hundreds is C, rounded to the nearest tens is D. We know that A<B<C<D<E. How many such 5-digit numbers are there?
B.1023. There are 6 different color balls in a box: red, yellow, green, blue, white, and black. We take balls out of the box one at a time without looking until we took the red ball out. We do not put balls back. How many different ways can we get to the red ball if the order of the balls taken out does matter?
B.1024. The sum of three different prime numbers is the square of a fourth, different prime. Every prime is less than 41, and you can write the first three primes using only three different digits. What is the product of the first three prime numbers?
by G.J. Radnai, PhD, Eotvos University, Budapest, Hungary
Please, send your solutions here.
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