Daily quiz #010 - can we replace the ?
Good day steemians
Honestly, it been almost a week now the daily quiz has not been active which is actually due to my inconveniences here.
But right now I guess am back and better and also with a new quiz
As we all know, only the best three commenters with the correct answer and explanation goes away with the bounty (SBD) I'm placing on this post. To know more about the steem bounty project, kindly check @steem-bounty blog.
Here are the Rules!
- All participants must upvote and comment on this post
- All participants must follow me
- Only the best three will be chosen
- After three days of this post, I will choose and announced the winners of this contest
- You are not allowed to edit your comment.
Also congratulations to the winners of the past quizzes.
98 - take the first number 64 add 6+4=10 then 64+10=74, 74 add 7+4=11 then 74 +11=85, 85 - 8+5=13 so 85+13=98, 98 - 9+8=17 so 98+17=115, then 115- 1+1+5=7 so 115+7=122
congratulations mate you won the quiz
Start with the number 64. Add them together and than add that answer to itself to get the next number (clockwise). Like this: 6+4=10 then 10+64=74
Followed by:
7+4=11 then 11+74=85
8+5=13 then 13+85=98
9+8=17 then 17+98=115
1+1+5=7 then 7+115=122
The missing number is 98
congratulations mate you won the quiz
Thanks for the puzzle!
The answer is 98 because 6+4=10 and 10+64=74 and if you do that with the followin numbers the answer is 98
6+4=10, 10+64=74
7+4=11, 11+74=85
8+5=13, 13+85=98.
Steps
Add the two digits(tens and unit) of the tens, then add the answer to the tens itself
Repeat the steps for others
OK, so the answers which suggest 98 all find a plausible pattern. But it has a couple problems: the sequence cannot be continued backwards, and there is no obvious reason for 64 to be the starting point either of the sequence or of the diagram.
The closest we can come to a predecessor for 64 using the "add the sum of digits" rules is:
64 - 9 = 55 (digit sum 10)
64 - 10 = 54 (9)
64 - 11 = 53 (8)
64 - 15 = 49 (13)
64 - 16 = 48 (12)
But what if the numbers actually form a cycle? What happens if we plot them as radial coordinates, evenly spaced?
ListPolarPlot[{{Pi/3,74},{0,85}, {-2*Pi/3,115},{- Pi,122},{2*Pi/3,64}},PlotRange->All, Joined->True]Obviously, they form points on a rectangle and we should fill in the missing point so that this pattern is maintained.
50 looks about right, but the line going from (0,85) to (-2*pi/3,115) in polar coordinates has equation
r cos t - (19 * sqrt*3 / 23) * r sin t - 85 = 0
At t = -pi/3 we have r = 398/8 = 48.875, which I submit as my answer.
(All of the above is, I should add, quite tongue-in-cheek.)
On a more serious note, I wrote an article about some of the math behind this puzzle: https://steemit.com/math/@markgritter/digit-sum-sequences
@mathematrix has set 0.150 SBD bounty on this post!
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The answer is 98 because you take the numbers separately
For example 74 is 7 and 4
Then you add these invdivudal numbers up
7+4
and get 11
so then you do 11+ 74 and you get 85
So by that logic the answer is
98
waw i really love the logic
Here the way can be solved.
first, 74+(7+4)=85
as same, 85+(8+5)=98
cheak the way the number is correct or not
122-115=7=(1+1+5)
115-98=17=(9+8)