## 5th and 6th Grade, December, 2018

B.1217. On a Christmas tree there are ornaments in the shape of a star, a sphere or an icicle. The mass of a sphere is equal to the mass of a star and 3 icicles. The mass of 2 stars is equal to the mass of a sphere and 2 icicles. The mass of how many icicles is equal to the mass of one star?

B.1218. Suppose 20 students participated on the school’s ski trip. We know that 4 of them had exactly one sibling on the trip, 9 students had exactly 2 siblings on the trip, and 7 students went on this trip without a sibling. Upon arrival from this trip everybody’s mother was there. How many mothers were waiting for their children?

B.1219. Find all those 3-digit numbers that when you add to and subtract from it the sum of its digits, you get a number with identical digits.

B.1220. The mechanical date indicator of a watch shows the days of a month from 1 to 31 by every day progressing one number (31 is followed by 1 again). At the end of each month having less than 31 days we have to turn this counter forward so that the watch would show the correct number indicating the actual day of the month. On February 28, 2009, we decided that we will not forward the date indicator anymore ever again. From that day, when did the watch show the correct date again for the first time?

B.1221. To measure the heights of the family members, the Sillywillie family bought a measuring rod with centimeter divisions on it, which has “80 cm” written on it at one end, and “170 cm” at the other end. (The person being measured is always standing on the floor, therefore, you can measure people whose heights are between 80 cm and 170 cm when the rod is used properly.) So, they nailed the rod onto the wall in a vertical position. However, they forgot to check where the bottom of the rod is on the wall, and they also forgot to check which end of the rod is at the bottom. This way the 130-cm-tall Pete, standing on the floor, measured in as 100 cm tall. At which mark on the rod would the top of the head of Pete’s sister be if she is 140 cm tall?

B.1222. Using 2 colors, we colored a 3×3 grid: one field is green and the rest is red, or 2 fields are green and the rest is red. How many different colored grids can you possible get? (Two grids are considered to be colored the same way if one of them can be rotated into the other.) B.1223. You received an assignment to multiply 123 by a 2-digit number in which one of the digits is twice as much as the other digit. Before the multiplication, by accident, you switched the two digits, therefore, the product is 3321 more than it is supposed to be. Which number were you supposed to multiply 123 by?

B.1224. 2018 could be written as 13202. Explain!