Missing number in a wheel
Missing number in a wheel
§ Q. What is missing number in following wheel as described below ?
Pic 1
➤ Soln-1: The most talked solution to this problem is given by the following observation:
The solution is 26.
This is a well established solution of this problem. A YouTube reference is also available for this problem. One can check it at:
https://youtu.be/vtFEiQM-G5I?si=VZxnBFaPYNmbIz9E
➤ Soln-2: Second solution stems from following fact:
In the Pic 1, see the first quadrant and third quadrant in their outer circle opposite shells, we have
8+6 =14 and 4+10 = 14. Both are having constant values 14. In the corresponding inner circle 20+14 = 34 in the 3rd quadrant.
In the analogy, if we examine second and fourth quadrant with values in their outer circle opposite shells, we have
7+4=5+6= 11. Therefore assuming 4th quadrant would be greater than the second quadrant as third was greater than first, then value of "?" would be 37+11 = 48. Answer is 48.
➤ If in above we assume that second quadrant would be greater, then value of "?" would be 37-11 = 26; which is there in soln-1.
➤ Soln-3: Damping System It could be looked as Damping System with the following assumptions:
There are x() and y() along the lines of X-axis and Y-axis, which are there on outer circle and the resonant values r() are given inside the inner circle. So 4,6,10,5 which are along X-axis are x values as x1,x2,x3,x4 etc. Similarly correspondingly y values along Y-axis are 8,4,6,7 with n=1,2,3,4. The r(n) would be 20, ?, 34, 37 in that order.
Considering circular system after n=4, the n=1 repeats & vice versa, we can go by equation:
r(n) = x(n)*y(n-1) + ((-1)^n)*(y(n))
The answer comes out to be 52.
➤ Soln-4: A common rule that could also be seen, and that could be considered to resolve is to find this pattern as given by (2,6,4, y), where y is to be determined a-prioi as being observed as follows:
1st quadrant: (20-4)/8=2
2nd quadrant: (37-7)/5=6
3rd quadrant: (34-10)/6=4
4th quadrant: (x-4)/6=y => x=6y+4
Where y should fit in this pattern of (2,6,4, y). Therefore, by this method innumerable solutions would exist, provided we get a pattern satisfying some logic.
■If one takes y=8 as 8 missing in jumps of 2 in the pattern of (2,6,4, y), then x= 6*8+4=52
■If one takes y=12 as 6 is three times of 2,the missing in jumps would be three times of 4 in the pattern of (2,6,4, y); also it can be justified by observing 4 is double of 2, so y should be double of 6, then in that case x= 6*12+4=76.
Many more like this !!!
□ This pattern (2,6,4, y) theory states if the number y is integer in this pattern, then we cannot accept 14 & well established solution 26 as its soln because then y = (x-4)/6 = (14-4)/6 a non integer in the pattern for x=14, and y = (26-4) / 6 again a non integer in the pattern for x=26.
➤ The ChatGPT response to this problem is as below as per someone.
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