40 and 39 can be ignored temporarily because they can be made from smaller numbers. The remaining are 20-4, 20-3, 20+3, 20+4. With 4 arrows, you have 80 + 4 lots of +/- 3,4 in some combination. With 5 arrows, it's 100 + 5 smaller bits, and with 6 arrows it's 120 +/- 6 smaller bits. Only with 6 arrows can you get the +/- to exactly match up to get you to 100. And you can't merge any pairs of them back into the 39 and 40 arrows.
I always pause the video, and I try to 'think logically', but often don't see the right path to follow, but I always try, and with this one I got this right away. Your vids help a lot, thanks.
Notice that each score can be written as A) nx5+1 or B nx5+2 also notice that 100= 20x5 to reach 20x5 we have to add either A+B+B or A+A+A+B only in these cases you can fom extra groups of five. with any other combination will be impossible to form 20 groups of five.
Ahha, so there really is just a bruteforce method. Thank you~ That said, the reply at the end really was nicely formatted! Definitely impossible since I'm on mobile though haha.
Two arrows on 40 and one arrow exactly on the line between the 17 zone and the 23 zone. (We are already assuming an archer with perfect accuracy, right? That's necessary for the problem.) An arrow on the line should be awarded the average points of the two zones: (17 + 23)/2 = 20. Hence, 40 + 40 + 20 = 100.
One more soln 16 17 a b 23 24 c d 39 40 e f 16a +17b .... = 100 St a to f all non negative. Replace 16(a+b) + b Is like 16x + y St x>=y Same for 23 and 39 So need to make no less than 100 by 16 23 and 39 One soln by 16 Then easily move through 16 replace by 23 or 39 Faster results....
@@shashwatgupta4613 thanks for taking time to respond. Would you please share the solution in detail as I found it a little difficult to understand. Your comment is highly appreciated.
![Spot The Difference: Test Your Memory Skills Now! [Find The Difference]](/img/n.gif)
40 and 39 can be ignored temporarily because they can be made from smaller numbers. The remaining are 20-4, 20-3, 20+3, 20+4. With 4 arrows, you have 80 + 4 lots of +/- 3,4 in some combination. With 5 arrows, it's 100 + 5 smaller bits, and with 6 arrows it's 120 +/- 6 smaller bits. Only with 6 arrows can you get the +/- to exactly match up to get you to 100. And you can't merge any pairs of them back into the 39 and 40 arrows.
@@SimonClarkstone that was a fantastic perspective ❤️
I noticed that 100/6 is about 16.67, meaning some combination of 16s and 17s will do the trick.
From there it's just guess and check
Good one 👌
Bro Post a video regularly
Yes bro… now back to work 😁… well recently posted two more videos, in case if you missed !
@LOGICALLYYOURS sorry I missed that 😅
I always pause the video, and I try to 'think logically', but often don't see the right path to follow, but I always try, and with this one I got this right away. Your vids help a lot, thanks.
That’s amazing… you are a logical thinker!
@@LOGICALLYYOURS 😎
Well I saw 6 16s is 96, and 17 is one more, so replace 4 16s with 17s to get 4 more which is 100.
16+16+17+17+17+17=100
Nice and Simple
Notice that each score can be written as A) nx5+1 or B nx5+2 also notice that 100= 20x5 to reach 20x5 we have to add either A+B+B or A+A+A+B only in these cases you can fom extra groups of five. with any other combination will be impossible to form 20 groups of five.
Nice one, keep it up.😊
isnt this basic dynamic programming?
I got it right.
6x16 = 96. So 4 more is needed, so 4 of the 16s turn to 17s.
Or 100/3=33 1/3. 3(16+17)=99. change one 16 to a 17 and you now get 100.
Ahha, so there really is just a bruteforce method. Thank you~
That said, the reply at the end really was nicely formatted! Definitely impossible since I'm on mobile though haha.
It's all about finding the pattern, sometimes a brute force approach is the best way to do that!
@@LOGICALLYYOURS atleast with his tips it reduced it from 7⁵ ish possible combinations to about 12 which is very optimized.
Thank you again~
17*4 + 16*2
Two arrows on 40 and one arrow exactly on the line between the 17 zone and the 23 zone. (We are already assuming an archer with perfect accuracy, right? That's necessary for the problem.) An arrow on the line should be awarded the average points of the two zones: (17 + 23)/2 = 20. Hence, 40 + 40 + 20 = 100.
4x17 + 2x16.
16, 16, 17, 17, 17, 17
I solve it previous week
That’s great Nikhil… in this video i was trying to explain checking other combinations
Treat after a long time , expecting more
Yes Srikanth, more puzzles on their way… by the way, did you check out previous two puzzles posted in the last week
4 times 17 2 time 16
One more soln
16 17 a b
23 24 c d
39 40 e f
16a +17b .... = 100
St a to f all non negative.
Replace
16(a+b) + b
Is like 16x + y
St x>=y
Same for 23 and 39
So need to make no less than 100 by 16 23 and 39
One soln by 16
Then easily move through 16 replace by 23 or 39
Faster results....
@@shashwatgupta4613 thanks for taking time to respond. Would you please share the solution in detail as I found it a little difficult to understand. Your comment is highly appreciated.