## 5th and 6th Grade, January, 2020

B.1281. In the following addition the same letters mean the same digit, and different letters mean different digits. What are the values of the different letters?

AAA + BBB + CCC = BAAC

B.1282. Kate created a 3×3 grid. She wrote positive whole numbers in its fields so that if you pick three numbers from the grid, so that no two are in the same column or row, then the product of these three numbers will always be the same. How many different ways can you fill in the blank fields?

B.1283. Fill in the blanks of the following grid, using the digits 1, 2, 3, and 4, so that each column and each row would have one of each of these digits.

B.1284. Thelma has eight 1x1x1 cubes that are painted white on all sides. Pete told her that he could paint just two 1×1 sides blue so that she could not make an all-white 2x2x2 cube using these cubes anymore. Is Pete telling the truth? If yes, what sides should he paint blue?

B.1285. There are 8 points on the circumference of a circle so that any two neighboring points are at the same distance. How many different shape triangles can you draw whose vertices are 3 of these 8 points?

B.1286. My calculator shows the different digits by lighting up its square-shaped “points” in the following way:

For example: 19 points are lit up for the digit zero, and 21 points are lit up for the number 17. Find a 2-digit number that needs just as many “points” to be lit up as the number itself when shown on my calculator.

B.1287. Andrew, Ben and Cole are playing with a pile of pennies by the following rules: if the number of pennies in the pile is even then Andrew gets half of the pennies; if the number of pennies in the pile is odd, then Cole gets a penny and Ben gets half of the rest of the pennies in the pile. They continue playing this game until they run out of pennies in the pile.

a) How many pennies do each player get if they start with a pile of 2020 pennies?

b) How many pennies did they start with (between 2000 and 3000) if Cole got only 1 penny in the entire game?

B.1288. Using the least amount of parentheses possible in the following expression, get 6 as a result of the operations.

1 : 2 : 3 : 4

( : means division)