Grades 5-6 Video Solutions 2024-2024_5-6

Video Transcription

Question 16. The Braille system is used by people who are blind. When written down, the digits 0 through 9 are represented by a set of black and white dots as shown.  How many different two-digit numbers contain exactly five black dots? First, let's group up all the numbers based on how many dots they have.  We have one number with one dot, four numbers with two dots, four numbers with three dots, and one number with four dots.  From here, we have four different cases to make a five-dot two-digit number.  Case 1. We have one dot in the tens place and four dots in the ones place. We have one digit with one dot and one digit with four dots, giving us one number for this case.  Case 2. We have two dots in the tens place and three dots in the ones place. We have four digits with two dots and four digits with three dots, giving us 16 numbers for this case.  Case 3. We have three dots in the tens place and two dots in the ones place. This case is special, since while 0 has three dots, we cannot put it in the tens place, as that will cause our number to be a one-digit number instead of a two-digit number.  This means we have three valid digits with three dots and four digits with two dots, giving us 12 numbers for this case.  Case 4. We have four dots in the tens place and one dot in the ones place. We have one digit with four dots and one digit with one dot, giving us one number for this case. Adding up all our numbers from each case gives us 30 different two-digit numbers.

Video Summary

The Braille system uses a set of black and white dots to represent digits, and the task is to determine how many two-digit numbers can be formed with exactly five black dots. The numbers are grouped by their dot configurations. There are four cases to consider:<br /><br />1. One dot in tens place, four dots in ones place: 1 number.<br />2. Two dots in tens place, three dots in ones place: 16 numbers.<br />3. Three dots in tens place, two dots in ones place (excluding 0 in tens): 12 numbers.<br />4. Four dots in tens place, one dot in ones place: 1 number.<br /><br />Summing up gives a total of 30 different two-digit numbers.

Keywords

Braille system

two-digit numbers

black dots

dot configurations

mathematics