## 5th and 6th Grade, September, 2017

B.1137. Ann and Bea weigh 22 kg together, Ann and Cecilia together weigh 28 kg, while Bea and Cecilia together weigh 36 kg. How much do they each weigh alone?

B.1138. How many 3-digit positive whole numbers do not contain the digits 2 and 9?

B.1139. Agnes, Sylvia, Pete and Leslie are classmates. They all have different family names: Smith, Miller, Taylor and Woo. In each of the following pairs of names one name is correct, but the other is not. What are the correct names?

1. a) Leslie Smith and Sylvia Miller
2. b) Leslie Miller and Sylvia Taylor
3. c) Agnes Miller and Pete Taylor

B.1140. The calculator uses 7 lines to show the digit 8. (See the diagram.) The other digits are shown by using some of these lines, as we know. Some of the 2-digit numbers are shown on the calculator by using exactly as many lines as the sum of their digits. How many such 2-digit numbers are there?

B.1141. A tea factory puts a little card in each tea box that either says Bermuda, Hawaii, or Fiji. If you send in 4 cards saying Bermuda, or 3 cards saying Hawaii, or 2 cards saying Fiji, you can participate in a lottery and win a trip to the island on the card. How many boxes of tea do you have to buy at least if you want to participate in the lottery for sure?

B.1142. On a farm they keep black and white goats and black and white sheep. Two shepherds take 50 animals out with them to the meadow. On the way there, one of the shepherds counts the number of white animals, and the other shepherd counts the number of sheep. From these two numbers they want to know how many black goats and white goats and how many black sheep and white sheep are there with them. Give an example when they can, and give an example when they cannot do it.

B.1143. There are five unicorns in a zoo eating a total of 5 rolls of hay every week. Every white unicorn eats 2 rolls of hay a week, every black unicorn eats a half a roll a week, and every Asian unicorn eats a quarter of a roll of hay every week. How many white, black and Asian unicorns are there in this zoo?

B.1144. What is the angle between the two hands of an analog clock at 10 minutes past 6 o’clock?