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1. BMAD's post in Bringing back an old one.... Making Toast was marked as the answer
Solution
https://www.simonsfoundation.org/multimedia/mathematical-impressions-multimedia/the-bicycle-pulling-puzzle/
3. BMAD's post in points in a plane was marked as the answer
I have

4. BMAD's post in Take the last chip was marked as the answer
Well done!
6. BMAD's post in A simple multiple-choice test was marked as the answer
I got (depending on the definition of answer)
8. BMAD's post in Five Points on a Sphere was marked as the answer
9. BMAD's post in Which clock would you prefer? was marked as the answer
10. BMAD's post in Rats and cats was marked as the answer
11. BMAD's post in Maybe factoring a polynomial completely was marked as the answer
ac = 2
bd = -2
c - a = -1
d - b = 3

d = 3 + b
b(3+b) = -2
b2+3b+2 = 0
(b+2)(b+1) = 0, b = -2 and d = 1 or b =-1 and d=2

c - a = -1
c = -1 + a
ac = 2
a(-1+a)=2
a2-a-2=0
(a-2)(a+1)=0; a=2 and c =1 or a=-1 and c=-2

b = -2 and d = 1 or b =-1 and d=2
a=2 and c =1 or a=-1 and c=-2

ad = 4 or 2 or -1 or -2
bc = -2 or 4 or -1 or 2

given:

ad = 4 when bc = -1 so a = 2, d = 2, b = -1, c = 1
ad= -1 when bc = 4 so a = -1, d = 1, b = -2, c = -2

12. BMAD's post in More triangles in circles was marked as the answer
13. BMAD's post in Forming a regular hexagon from a lattice was marked as the answer
14. BMAD's post in How do you shuffle cards? was marked as the answer
15. BMAD's post in Maximum absolute or absolute maxima was marked as the answer
17. BMAD's post in Greatest Common Factor and Least Common Multiple was marked as the answer
19. BMAD's post in Sum of n consecutive integers was marked as the answer
21. BMAD's post in Line through a circle was marked as the answer
these are the solutions. Well done everyone!
22. BMAD's post in Shuffling a Deck of Cards was marked as the answer