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Congrats to the two who obtained the correct answer in POTW #30. Please see my reply to POTW#30 for the correct answer. If you obtained something different, do you see why or how you did?
In order to make sure that Arvil wins on her third turn, she could place a 9 on the question mark. This is because no matter what Bob does she has a way of getting 15 with 9 out of the way. If she didn't put 9, Bob could have put 9 so he doesn't lose because 6+9 is already 15, Therefore if Bob put anything from 1, 2, 4, 5, 7, or 8, she could put 8, 7, 5, 4, 2, or 1.
To find this I looked at the actual game and wrote down all the numbers that we could possible work with. These included: 1,2,4,5,7,8 and 9. So I put 4 into the circle, this meant that Bobs combinations could only consist of 1,2,5,7,8,9.
Say bob decided to put in a 2. Avril could easily counter that with a 7.
Next, I tried 5.
This meant that the only possible numbers for Bob would be 1,2,4,7,8,9.
Lets assume that he puts a 1. This means that Avrils next move can be 8.
I continued doing this procedure and found out that we cannot use numbers like 1 ( as it wont work with all the numbers from 2,4,5,7,8 and 9, but only from 2,4,5, and 7) ,3,6.
Finally, I found that there are 6 nubers that could go into the ?.
Actually, he can only put one number which would be 9, this is because if Bob decides to put a 9 on his second turn the there is no way that Arvil can get the point on her third term.
The possible numbers that Avril could place are 1,2,4,5,7,8,9 as 3, and 6 are already placed. The number he would place would be a 9 as all combinations can be made. For example, If avril were to place a 9 and Bob were to place:
- A 1 then 1+6 = 7 and Avril could win by placing a 8 - A 2 then 2+6 = 8 and Avril could win by placing a 7 - A 4 then 4+6 = 10 and Avril could win by placing a 5 - A 5 then 5+6 = 11 and Avril could win by placing a 4 - A 7 then 7+6 = 13 and Avril could win by placing a 2 - A 8 then 8+6 = 14 and Avril could win by placing a 1
All of these wok as possible combinations for the third turn. DOING IT AGAIN AND AGAIN.
The possible numbers that Avril could place are 1,2,4,5,7,8,9 as 3, and 6 are already placed. The number he would place would be a 9 as all combinations can be made. For example, If avril were to place a 9 and Bob were to place:
- A 1 then 1+6 = 7 and Avril could win by placing a 8 - A 2 then 2+6 = 8 and Avril could win by placing a 7 - A 4 then 4+6 = 10 and Avril could win by placing a 5 - A 5 then 5+6 = 11 and Avril could win by placing a 4 - A 7 then 7+6 = 13 and Avril could win by placing a 2 - A 8 then 8+6 = 14 and Avril could win by placing a 1
All of these wok as possible combinations for the third turn. DOING IT AGAIN AND AGAIN.
In order to make sure that Arvil wins on her third turn, she could place a 9 on the question mark. This is because no matter what Bob does she has a way of getting 15 with 9 out of the way. If she didn't put 9, Bob could have put 9 so he doesn't lose because 6+9 is already 15, Therefore if Bob put anything from 1, 2, 4, 5, 7, or 8, she could put 8, 7, 5, 4, 2, or 1.
ReplyDeleteThe possible moves are 4,5,7,8,2, and 9.
ReplyDeleteTo find this I looked at the actual game and wrote down all the numbers that we could possible work with.
These included: 1,2,4,5,7,8 and 9.
So I put 4 into the circle, this meant that Bobs combinations could only consist of 1,2,5,7,8,9.
Say bob decided to put in a 2. Avril could easily counter that with a 7.
Next, I tried 5.
This meant that the only possible numbers for Bob would be 1,2,4,7,8,9.
Lets assume that he puts a 1. This means that Avrils next move can be 8.
I continued doing this procedure and found out that we cannot use numbers like 1 ( as it wont work with all the numbers from 2,4,5,7,8 and 9, but only from 2,4,5, and 7) ,3,6.
Finally, I found that there are 6 nubers that could go into the ?.
Actually, he can only put one number which would be 9, this is because if Bob decides to put a 9 on his second turn the there is no way that Arvil can get the point on her third term.
DeleteThe possible numbers that Avril could place are 1,2,4,5,7,8,9 as 3, and 6 are already placed. The number he would place would be a 9 as all combinations can be made. For example, If avril were to place a 9 and Bob were to place:
ReplyDelete- A 1 then 1+6 = 7 and Avril could win by placing a 8
- A 2 then 2+6 = 8 and Avril could win by placing a 7
- A 4 then 4+6 = 10 and Avril could win by placing a 5
- A 5 then 5+6 = 11 and Avril could win by placing a 4
- A 7 then 7+6 = 13 and Avril could win by placing a 2
- A 8 then 8+6 = 14 and Avril could win by placing a 1
All of these wok as possible combinations for the third turn. DOING IT AGAIN AND AGAIN.
The possible numbers that Avril could place are 1,2,4,5,7,8,9 as 3, and 6 are already placed. The number he would place would be a 9 as all combinations can be made. For example, If avril were to place a 9 and Bob were to place:
ReplyDelete- A 1 then 1+6 = 7 and Avril could win by placing a 8
- A 2 then 2+6 = 8 and Avril could win by placing a 7
- A 4 then 4+6 = 10 and Avril could win by placing a 5
- A 5 then 5+6 = 11 and Avril could win by placing a 4
- A 7 then 7+6 = 13 and Avril could win by placing a 2
- A 8 then 8+6 = 14 and Avril could win by placing a 1
All of these wok as possible combinations for the third turn. DOING IT AGAIN AND AGAIN.