## 3rd and 4th Grade, September

A.1193. Draw a triangle and a quadrilateral so that their sides would have the following number of points in common:

a) 1

b) 3

c) 5

d) 6

e) 7

A.1194. Could the sum of the squares of two consecutive positive integers be the square of a whole number?

A.1195. How many pieces can you possible get if you cut a vertical column with a rectangular base by three planes?

A.1196. At a village carnival you can buy local musical instruments with their local currency, which is dings and dongs. You can buy one ding for \$5, and one dong is worth 3 dings. A wooden recorder and a clay whistle together are worth the same as three mouth harps. Four wooden recorders and three mouth harps together are worth the same as two clay whistles. What is the price of each instrument in dollars if you can buy a wooden recorder for 4 dongs and 2 dings?

A.1197. Find the smallest prime number that is the sum of three different prime numbers.

A.1198. At the gingerbread stand there are three different figures you can buy: heart, doll and soldier. Every third figure is a heart, and every other heart has a mirror in the middle of it. Every fifth figure is a doll. I counted a total of 90 figures. How many of them is a heart with a mirror in the middle, and how many of them is a soldier?

A.1199. Inga bought 5 meters of linen and 2 meters of silk for \$36.60. Eva bought 7 meters of linen and 4 meters of silk for \$67.00. Veronica bought 3 meters of linen and 3 meters of silk. How much change did she get back from \$100.00?

A.1200. You may use a red and a blue pen, and you may write the digits 1, 2, or 3. How many different 6-digit numbers can you write down if every digit must be written either in red or in blue, but no two neighboring digits can be identical or of the same color?