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The only four combinations are: 3,3,3,3,2,2,0 5,5,3,3,0,0,0 2,2,2,2,2,3,3 5,5,2,2,2,0,0 Once I found all the combinations, now I need to find all the different orders I can make. By using factorials, I can determine the number of combinations I can make. The amount of combinations I could make is 526 combinations. Work done hardcopy I'm not sure if I did this question correctly.
I got the answer of 4 different combinations: 5+5+3+3+0+0=16 3+3+3+3+2+2+0=16 5+3+2+2+2+2=16 3+3+2+2+2+2+2=16 I did the work in my math book. Also POTW #11, I did it in my mathbook since I did not do it, and I did not understand POTW #10
GRaDe 7 Potw; I'm not sure if I did this question correctly. But to figure this out I first listed all of the options you can have. 5,3, (0) and 2. I then can see how many different combinations of these numbers that can make 16. After doing this i figured out that they're are 4 combinations of numbers. 3,3,3,3,2,2,0 5,5,3,3,0,0,0 2,2,2,2,2,3,3 5,5,2,2,2,0,0 As long as you get these numbers it is fine. Though whichever order in which you complete this task is also fine and varies. Not sure if we should figure the exact different point combinations (different darts for different points). I'm also wondering do you NEED to use all 7 darts? Cause on the question it doesn't say exactly. We could assume 0 is also equivalent to didn't hit and didn't use but i'm not sure. If it is it may vary and unbalance our numbers.
SO here's how I solved it: First I found how many three digit numbers had a digit sum of 5 in only one step: 104, 113, 122, 132, 140 203, 212, 221, 230 302, 311, 320 401, 410 500 In total, that is 15 different three digit numbers that have a digit sum of 5 in one step.
Next we find the three digit numbers that take two steps to get the digit sum of 5. Since the highest number that can be made in digit sum is 9+9+9 = 27, that means our two digit number must be smaller than 27 and have a digit sum of 5. The only numbers that fit are 14 and 23. Now we find all the tree digit numbers that have a digit sum of 14 ( noooooooo gonna take sooo longgg) 149 158 167 176 185 194 239 248 257 266 275 284 293 329 338 347 356 365 374 383 392 419 428 437 446 455 464 473 482 491 509 518 527 536 545 554 563 572 581 590 608 617 626 635 644 653 662 671 680 707 716 725 734 743 752 761 770 806 815 824 833 842 851 860 905 914 923 932 941 950 That's 70 numbers, ( welp ._.) Now we find the number of three digit numbers that have a digit sum of 23, 599 689 698 779 788 797 869 878 887 896 959 968 977 986 995
That's 15 numbers. So now we add that together to get the total number of three digit numbers that have a digit sum of 5 in two steps: 15 + 70 = 85. 85 three digit numbers have a digit sum of 5 in two steps. Now for three digit numbers that have a digit sum of 5 in three steps. Well no two digit number can have a digit sum of 23, and the lowest two digit number that can have a digit sum of 14 is 77 and the highest digit sum with a three digit number is 27 Meaning there is no three digit number that has a digit sum of 5 in exactly 3 steps. So int he end we add the number of three digit numbers that have a digit sum of 5 in one step and then two steps together 85 + 15 = 100 100 three digit numbers have a digit sum of 5 in three of fewer steps. ( that took me, a very long time T~T)
I got 100 numbers that have digit sum of 5 in three pr fewer steps. So how I did this was I first of all did the old guess and check way but I did make it a bit easier for me. I filtered the numbers that would equal to 5 and filtered them by steps. First I found how many had the digit sum of 5 with 1 step, then 2, then 3. After that I counted how many answers I got. Thus adding up to 100.
Here is how I went about solving the Grade 7 POTW:
I found that these six combinations all add up to 16: 2,2,2,2,2,3,3 2,2,2,2,3,5,0 3,3,5,5,0,0,0 3,3,3,3,2,2,0 5,5,2,2,2,0,0 5,5,3,3,0,0,0 I found these by just doing guess and check.
I used a tree diagram to help me, I ended up with four different combinations, but the order wasn't in play when I calculated this. 2,2,2,2,2,3,3 3,3,3,3,2,2,0 5,5,2,2,2,0,0 5,5,3,3,0,0,0
Also, why did only one grade 8 do the grade 8 one and like 7 grade sevens did the grade seven one... :/
To solve this question I wrote down all the possible combinations and found the sum of each. This way, I found all the possible ways to win the game and did miss any. Here are the different combinations that add up to 16.
3,3,3,3,2,2,0
ReplyDelete5,5,3,3,0,0,0
2,2,2,2,2,3,3
5,5,2,2,2,0,0
4 combinations excluding order exist.
Luke, for this question, I think that the order matters to determine all the point combinations. But I am not sure.
DeleteThe only four combinations are:
ReplyDelete3,3,3,3,2,2,0
5,5,3,3,0,0,0
2,2,2,2,2,3,3
5,5,2,2,2,0,0
Once I found all the combinations, now I need to find all the different orders I can make. By using factorials, I can determine the number of combinations I can make.
The amount of combinations I could make is 526 combinations. Work done hardcopy
I'm not sure if I did this question correctly.
I got an answer of 100 numbers with a digit sum of 5 that can be reached in 3 or less steps.
ReplyDeleteI got the answer of 4 different combinations:
ReplyDelete5+5+3+3+0+0=16
3+3+3+3+2+2+0=16
5+3+2+2+2+2=16
3+3+2+2+2+2+2=16
I did the work in my math book.
Also POTW #11, I did it in my mathbook since I did not do it, and I did not understand POTW #10
GRaDe 7 Potw;
ReplyDeleteI'm not sure if I did this question correctly. But to figure this out I first listed all of the options you can have. 5,3, (0) and 2. I then can see how many different combinations of these numbers that can make 16. After doing this i figured out that they're are 4 combinations of numbers.
3,3,3,3,2,2,0
5,5,3,3,0,0,0
2,2,2,2,2,3,3
5,5,2,2,2,0,0
As long as you get these numbers it is fine. Though whichever order in which you complete this task is also fine and varies. Not sure if we should figure the exact different point combinations (different darts for different points). I'm also wondering do you NEED to use all 7 darts? Cause on the question it doesn't say exactly. We could assume 0 is also equivalent to didn't hit and didn't use but i'm not sure. If it is it may vary and unbalance our numbers.
SO here's how I solved it:
ReplyDeleteFirst I found how many three digit numbers had a digit sum of 5 in only one step:
104, 113, 122, 132, 140
203, 212, 221, 230
302, 311, 320
401, 410
500
In total, that is 15 different three digit numbers that have a digit sum of 5 in one step.
Next we find the three digit numbers that take two steps to get the digit sum of 5.
Since the highest number that can be made in digit sum is 9+9+9 = 27, that means our two digit number must be smaller than 27 and have a digit sum of 5. The only numbers that fit are 14 and 23. Now we find all the tree digit numbers that have a digit sum of 14 ( noooooooo gonna take sooo longgg)
149 158 167 176 185 194
239 248 257 266 275 284 293
329 338 347 356 365 374 383 392
419 428 437 446 455 464 473 482 491
509 518 527 536 545 554 563 572 581 590
608 617 626 635 644 653 662 671 680
707 716 725 734 743 752 761 770
806 815 824 833 842 851 860
905 914 923 932 941 950
That's 70 numbers, ( welp ._.)
Now we find the number of three digit numbers that have a digit sum of 23,
599
689 698
779 788 797
869 878 887 896
959 968 977 986 995
That's 15 numbers.
So now we add that together to get the total number of three digit numbers that have a digit sum of 5 in two steps:
15 + 70 = 85.
85 three digit numbers have a digit sum of 5 in two steps.
Now for three digit numbers that have a digit sum of 5 in three steps.
Well no two digit number can have a digit sum of 23,
and the lowest two digit number that can have a digit sum of 14 is 77
and the highest digit sum with a three digit number is 27
Meaning there is no three digit number that has a digit sum of 5 in exactly 3 steps.
So int he end we add the number of three digit numbers that have a digit sum of 5 in one step and then two steps together
85 + 15 = 100
100 three digit numbers have a digit sum of 5 in three of fewer steps.
( that took me, a very long time T~T)
I got 100 numbers that have digit sum of 5 in three pr fewer steps. So how I did this was I first of all did the old guess and check way but I did make it a bit easier for me. I filtered the numbers that would equal to 5 and filtered them by steps. First I found how many had the digit sum of 5 with 1 step, then 2, then 3. After that I counted how many answers I got. Thus adding up to 100.
ReplyDeleteI did mine on paper. There are 4 different combinations.
ReplyDeleteHere is how I went about solving the Grade 7 POTW:
ReplyDeleteI found that these six combinations all add up to 16:
2,2,2,2,2,3,3
2,2,2,2,3,5,0
3,3,5,5,0,0,0
3,3,3,3,2,2,0
5,5,2,2,2,0,0
5,5,3,3,0,0,0
I found these by just doing guess and check.
I used a tree diagram to help me, I ended up with four different combinations, but the order wasn't in play when I calculated this.
ReplyDelete2,2,2,2,2,3,3
3,3,3,3,2,2,0
5,5,2,2,2,0,0
5,5,3,3,0,0,0
Also, why did only one grade 8 do the grade 8 one and like 7 grade sevens did the grade seven one... :/
In order to solve this question, I decided to just make a list of all possible combinations by guessing and checking, and count up the combinations.
ReplyDelete5,5,3,3,0,0,0
5,3,3,3,2,0,0
5,5,2,2,2,0,0
3,3,3,3,2,2,0
2,2,2,2,2,3,3
2,2,2,2,3,5,0
There are 6 combinations that add up to 16.
To solve this question I wrote down all the possible combinations and found the sum of each. This way, I found all the possible ways to win the game and did miss any. Here are the different combinations that add up to 16.
ReplyDelete5,5,3,3,0,0,0 -> 5+5+3+3+0+0+0 = 16
5,5,2,2,2,0,0 -> 5+5+2+2+2+0+0 = 16
5,3,3,3,2,0,0 -> 5+3+3+3+2+0+0 = 16
5,3,2,2,2,2,0 -> 5+3+2+2+2+2+0 = 16
3,3,3,3,2,2,0 -> 3+3+3+3+2+2+0 = 16
3,3,2,2,2,2,2 -> 3+3+2+2+2+2+2 = 16
As you can see, all of these combinations have 7 numbers and add up to 16. (sorry for doing it late).