5th and 6th graders

November, 2014

 
B.985. One year two deadlines of a school's monthly math challenge fell on a Monday in October and in November. The date of the day in November is 5 times the date of the day in October. What days were these two deadlines?

B.986. There are a total of 2014 red, blue, white and yellow balls in a box. We pick a few of them randomly. In order to make sure that we have at least one ball from each color, we have to pick at least 1661 balls. What is the largest number of balls of the same color that could be in the box?

B.987. Each of two explorers could carry with him enough food for 12 days, and can walk 30 km a day. 300 km inwards from the edge of the desert, where they are, is a spot where they want to post a flag. Can they do it so that both explorers could get back to the edge of the desert alive?

B.988. There is a 1530 cm long ribbon. We want to cut it up into 30 cm and 24 cm pieces, so that we would not waste any of the ribbon, but have at least one of each size of pieces. How many of each size should we cut?

B.989. How many 3-digit numbers have at least 2 identical digits?
B.990. You can see the crossection of a vase on the diagram. What is its area if the side of a little square on the diagram is 2 cm? (Each curved line is a half or a quarter of a circle.)
B.991. Starting from the origin, a spider is crawling on the lines of a (vertical-horizontal) square grid. What we can see from the outside is that first it goes to the right by 1 unit, then it goes up 2 units, then it goes left 3 units, then it goes down 4 units, then it goes right 5 units, up 6 units, left 7 units down 8 units, and so on. After every left turn, it goes one more unit in that direction than it went in the previous direction. Where is the spider after crawling the 2014th section?

B.992. Is it true that if we pick any 33 numbers out of the first 50 positive whole numbers then among the 33 numbers there will always be two numbers such that one of them is twice the other?
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