## 7th and 8th Grade, January, 2019

C.1225. Winnie-the-Pooh would like to invest \$1000. The Rabbit and Co. (Friends, Relatives, and Business Associates) Bank offers 4% interest in the first year, and then promises to increase the interest rate by 1% in each of the next 3 years. After the fourth year it will not change the interest rate. The Eeyore and His Tail Bank offers 5% interest every year, and that after every 5 years the bank will give a 7% bonus on the amount in the account (after the actual annual interest is added). Both banks would take the investment for no more than 10 years. Both banks adds the annual interest to the account at the end of the year. Winnie-the-Pooh does not know yet how many years he wants to invest his money for, but he would not want to take the interest out annually. Depending on the number of years of investment, which bank offers a better deal to Winnie-the-Pooh?

C.1226. In a weekend soccer league every team plays every (other) team exactly once. The head of the league just finished the schedule of the games when a few more teams joined the league. Now he had to schedule 37 more games. How many teams were there originally, and how many new teams joined the league?

C.1227. In Cowland there are two milk bars. At both, you can order Foamy Cocoa. At both they serve the Foamy Cocoa in a cylinder-shaped mug with the same height. (Half of the volume of the Foamy Cocoa is liquid cocoa, the other half is cocoa foam. In a short while, the foam becomes a quarter-of-its-volume-worth-of liquid cocoa.) At the Happy Cowboy, they serve Foamy Cocoa in a 6 cm radius mug for 12 petaks. At the Silly Sheppard they serve it in 5 cm radius mugs, but when the foam is all gone, they refill your mug. All this for 11 petaks. In which milk bar is the cocoa cheaper?

C.1228. The Eskimos greet each other with a nose rub, and they greet the Arctic researchers with a “high five”. The researchers say hello to the Eskimos, just as they greet each other. At a party at the North Pole, while everybody greeted everybody in the proper way, you could hear 415 hello’s. How many nose rubs and how many high five’s happened?

C.1229. A company asked a designer to come up with a trade-sign. The designer used 2 different regular hexagons, and this is how he came up with his final proposal. (See diagram below.) What is the ratio of the areas of the gray and the white regions in the diagram on the right?

C.1230. Antarc Tica, the Polar researcher, who got stuck on Antarctica, last month during the very cold nights burned 3 more maps than wooden spoons, 5 more pairs of wooden skis then boxes of matches, one more barrel of seal fat than the number of maps he burned, and four times more wooden skis than wooden spoons and barrels of seal fat together. How many items did he burn if he left only one box of his 16 boxes of matches? (One pair of skis is considered to be two pieces of items, one barrel of seal fat and one box of matches each is considered to be one item.)

C.1231. What number is 50% more than the number that is 25% less than the number that is 60% more than 10?

C.1232. The sides of the squares on the diagram below are 2cm, 3cm, and 5cm. How many square centimeters is the area of the shaded triangle ACG?