Grades 1-2 Video Solutions 2023-2023_1-2

Video Transcription

Problem number 24. Digits 1, 1, 2, and 3 are printed on four different cards. Three cards are laid out to make a subtraction, as shown in the picture.  How many different results can we get? The digits are 1, 1, 2, and 3. So we can use the digit 1 twice within this subtraction, but all the other digits can only be used once.  Notice that the problem asks how many different results we can get. That means that we will have to figure out the subtractions  in order to see if there are any repeats of the results. To solve this problem, we're going to have to list our options and find the results.  Since the first number is a two-digit number, let's make a list first of what the two-digit number could be. If the tenth digit is 1, then the ones digit could be a 1,  which makes 11, 2 for 12, or 3 for 13. If the tenth digit is 2, we can only make 21 or 23, because there's only one 2 to be used.  And if the tenth digit is 3, we can only make 31 or 32. So we can only make 11 minus 2 or 11 minus 3. And let's go ahead and do the math right now.  11 minus 2 is 9, and 11 minus 3 is 8. If we use 12 as our first number, we can have 12 minus 1, because we do have another 1, which is 11, or 12 minus 3, which gives us 9.  And we already see that we have the number 9 twice as a result, so we'll have to ignore this when we count how many different results we have.  If the two-digit number is 13, we can have 13 minus 1, which is 12, or 13 minus 2, which is 11. And again, we have a repeated result. 11 here, 11 here.  So, so far, we have 1, 2, 3, 4 different results. If the two-digit number is 21, then we can subtract 1 from it for a result of 20, or we can subtract 3, which gives us 18.  With 23, we can do 23 minus 1, and that gives us 22. We can't do anything else with the 23, because you already used both the 2 and the 3. So that's three more different results.  If we do 31, we can do 31 minus 1, which is 30, or 31 minus 2, which is 29. With 32, just do 32 minus 1, which is 31, and this gives us three more different results.  So we have 4 plus 3 plus 3, or 10 different results. The answer is C.

Video Summary

The problem involves arranging digits 1, 1, 2, and 3 on cards to create different subtraction results. Considering each calculation and eliminating duplicates, the possible two-digit numbers are 11, 12, 13, 21, 23, 31, and 32. Performing all possible subtractions, you derive unique results: 9, 8, 11, 12, 20, 18, 22, 30, 29, and 31. Eliminating duplicates, a total of 10 unique results are identified. Thus, the solution yields 10 different results. Answer: 10.

Keywords

arranging digits

subtraction results

unique results

two-digit numbers

math problem