Mathematical Solutions To Problems I, II And III

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Author: Adekola Taylor
January, 2015

(1) Solution to Problem I


Number of columns, (C) = 5, number of cards in each column = 48,828,125
Number of cards in the arrangement, n(E) = 5 x 48,828,125
= 244,140,625
Since n (E) could be expressed in term of Cxe
then n(E) = Cxe = Cte/2
te = even regenerative distribution number
xe = even exponential number
This implies 244,140,625 = 5xe
then 5xe = 5te/2
Therefore, 244,140,625 = 512
512 = 5te/2
12 =te/2
te = 24

(2) Solution to Problem II


Number of columns, (C) = 12, number of students in each column = 10
Number of students in the arrangement, n(E) = 120
Since n (E) could be expressed in term of Ce[Ce - 2]
then n(E) = Ce[Ce - 2] = 1/4[te]2- 1
te = even regenerative distribution number
Ce = even column number
120 = 12[10] = 1/4[te]2- 1
480 =[te]2- 4
te = -22 or 22
Since we are dealing with concrete things
then te = 22
The regenerative distribution number (t) = 22

(3a) Solution to Problem III


Number of columns, (C) = 19, number of cards in each column = 21
Number of cards in the arrangement, n(E) = 399
Since n (E) could be expressed in term of Co[Co + 2]
then n(E) = Co[Co + 2] = [te]2- 1
te = even regenerative distribution number
Co = odd column number
Since te = so + 1
so = The last transposed version distribution number of the starting distribution
then, Co[Co + 2] = [so]2 + 2so
n(E) = 399 = 19[21] =[so]2 + 2so
[so]2 + 2so - 399 = 0
so[so + 21] - 19 [so + 21] = 0
[so + 21][so - 19] = 0
so = -21 or 19
Since we are dealing with concrete things
then so = 19
The last transposed version distribution number of the starting distribution = 19

(3b) Solution to Problem III


If the number of columns and rows were interchanged
then,number of columns, (C) = 21, number of cards in each column = 19
Number of cards in the arrangement, n(E) = 399
Since n (E) could be expressed in term of Co[Co - 2]
then n(E) = Co[Co - 2] = [te]2 - 1
te = even regenerative distribution number
Co = odd column number
21 X 19 =[te]2 - 1
399 + 1 =[te]2
te = -20 or 20
Since we are dealing with concrete things
then te = 20
The new regenerative distribution number (t) = 20

Click here for solutions to Problems IV and V

Click here to go back to Problems I - IV

References

  1. Taylor, Adekola A. (2016). Derivation of formulas for position change of entities in power inductive distribution. International Journal of Scientific and Research Publications 6(7):409-420.

  2. Taylor, Adekola A. (2015). Quadratic distribution patterns in Kola analysis. Mathematical Theory and Modeling 5: 60-66.

  3. Taylor, Adekola A. (2015). Derivation of formulas for position change in Kola analysis. International Journal of Scientific and Research Publications 5(11):101-109.

  4. Taylor, Adekola A. (2014). Logical-mathematical intelligence for teens. Mathsthoughtbook.com

  5. Taylor, Adekola A. (2013). Regenerative mathematics and dimurelo puzzles for children 8-12yrs. USA: Lulu Press Inc.

  6. Taylor, Adekola (2013). Card magic and my mathematical discoveries. USA:Lulu Publishing.

  7. Taylor, Adekola A. (2010). Kola Analysis: An inventive approach to logical-mathematical intelligence for secondary and advanced levels. Journal of Mathematical Sciences Education 1(1): 44-53.<

      Recommended Readings:

      1. Regenerative Mathematics

      2. Card Mathematical Intelligence Games

      3. Dimurelo Puzzles

      4. Simple Dimension Positiomatics

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