$ 不定方程式的正整數解 $

$ Alan $

$ Bob $

$ Cara $

$ Dora $

$ Eden $

$ Fay $

$ Gary $

$ Hedy $

$ Ian $

$ Jane $

A = (-0.64, 3.66)
B: A + (15, 0)
r = Distance(A, B)
n = 7 (slider from k to 10, step 1)
list1 = Sequence((x(A) + (i - 1) * r / 13.5, y(A)), i, 1, n + 1)
list11 = First(list1, n - 1)
k = 4 (slider from 3 to 6, step 1)
C: A - (0, 3.5)
D: B - (0, 5)
list3 = Sequence((x(A) + (i - 1) * r / 13.5, y(A) - 3), i, 1, k + 1)
t_q: "$試求方程式：\; " + (LaTeX["x_1+x_2" + (If[k ≟ 3, "+x_3", If[k ≟ 4, "+x_3+x_4", If[k ≟ 5, "+x_3+x_4+x_5", If[k ≟ 6, "+x_3+x_4+x_5+x_6", If[k ≟ 7, "+x_3+x_4+x_5+x_6+x_7", If[k ≟ 8, "+x_3+x_4+x_5+x_6+x_7+x_8", If[k ≟ 9, "+x_3+x_4+x_5+x_6+x_7+x_8+x_9", If[k ≟ 10, "+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}"]]]]]]]])]) + " =" + (LaTeX[n]) + "\;的正整數解$"
s = 3 (slider from 0 to 6, step 1)
text1: "$ 我們考慮將" + (LaTeX[n]) + "個相同的球，\;分給" + (LaTeX[k]) + "個人，\;每人至少一個 $"
text2: "$ 我們先分給每人一個球，\;剩下" + (LaTeX[n - k]) + "個相同的球，\;分給" + (LaTeX[k]) + "個人，\;每人可兼得或不得$"
p = Distance(Element[list3, 2], Element[list3, 1])
poly1, a_1, b, c, d = Polygon(A + (n * p, 0), Element[list1, n - k + 1], Element[list1, n - k + 1] + (0, p), A + (n * p, p))
E: C - (0, p)
list4 = Sequence((x(A) + (i - 1) * r / 13.5, y(E)), i, 1, k + 1)
poly2, e, f, g, h = Polygon(A + (n * p, 0), Element[list1, n - k + 1], Element[list1, n - k + 1] + (0, p), A + (n * p, p))
J = (12.1, 1.58)
K: J + (0.3, 0.3)
L: J + (0, 0.7)
M: L + K - J
J_1: J + (0.05, 0)
M_1: M + (0.05, 0)
L_1: L + (0.05, 0)
K_1: K + (0.05, 0)
list2 = Shuffle(list11)
a = -3.3 (slider from -5 to 5, step 0.1)