## 5th and 6th grade, March

B.1185. You write either + or -­ signs between the numbers in the sequence 1; 2; 3; 4; 5; … so that you would get 2018 as a result as soon as possible. What is the lowest possible number in the sequence we have to go up to?

B.1186. There are 11 girls and 16 boys in a class. Their math teacher gives them 20 problems. Each problem is given to either a boy, or a girl, or a boy-girl couple. Each problem is given out only once, and each student has to work on only one problem. How many boys and how many girls receive a problem on their own?

B.1187. How many 2-digit positive whole numbers are equal to the square of the sum of their digits?

B.1188. We would like to cut up a rectangular pan of cake into rectangular pieces. First we make a few cuts parallel to two opposite sides of the pan, then we make a few cuts perpendicular to these. We made a total of 13 cuts. Could the number of pieces be:

a) 45

b) 50?

B.1189. Using five identical digits, parentheses, and a few mathematical operations, create the number 30 in as many different ways as possible.

B.1190. In the following numbers: 1-a, 2-­a, 3-­a, …, 2018-­a, what should we substitute for “a” if the sum of these numbers is 17153?

B.1191. Some square numbers remain squares even if you write an extra digit 1 at the end of the number. Find the smallest such positive square number.

B.1192. Write down the positive 2-digit numbers in an increasing order by using blue, red, and green pen in this order continually for the digits. What is the color of the last digit 7 you have to write down?