[Community Puzzle] Particle Detection with Cloud Chamber

Puzzles
13

Hi Djoums,
I am not sure to understand where your problem came from, maybe it is because of my error in the statement with «nearest tenth» instead ef «the nearest multiple of 10».
Before writing this answer, I was sure that the abs(q)/m particle interval does not overlap as I choose the value .5 for the threshold of abs(g_p - G) / G such as, but my bad, abs(q)/m interval of proton and alpha overlap :expressionless: :rage: :pleading_face: :cry: :thinking: !

e-   : q = -1, m =    0.511  ==>  abs(q)/m =     1.96  :  G ∈ [   0.978,     2.94]
p+   : q =  1, m =  938.000  ==>  abs(q)/m =  0.00107  :  G ∈ [0.000533,   0.0016]
n0   : q =  0, m =  940.000  ==>  abs(q)/m =        0  :  G ∈ [       0,        0]
alpha: q =  2, m = 3727.000  ==>  abs(q)/m = 0.000537  :  G ∈ [0.000268, 0.000805]
pi+  : q =  1, m =  140.000  ==>  abs(q)/m =  0.00714  :  G ∈ [ 0.00357,   0.0107]

I took this criterion as a detail, but the devil is in the details!

So maybe I should change the statement

Likewise, the ratio g = |q|/m could not be computed exactly. Let’s note g_p the theoritical value of particle p (given in the table below) and G the computed value from picture with the formula above.
If
abs(g_p - G) / g_p < .5
one can conclude that the particle which just passed through the cloud chamber was p .
If none of the five known particle satifies
abs(g_p - G) / g_p < .5
one can conclude that the particle which just passed through the cloud chamber is unknown.

for

Likewise, the ratio g = |q|/m could not be computed exactly. Let’s note g_p the theoritical value of particle p (given in the table above) and G the computed value from ASCII-art picture with the formula above.
The particle p which just passed through the cloud chamber is the one with the minimal value of
abs(g_p - G) / g_p
if this value is stricly below .5, i.e. :
abs(g_p - G) / g_p < .5
If G is such that
abs(g_p - G) / g_p >= .5
for every known particles (those in the table above), one can conclude that the particle which just passed through the cloud chamber is unknown (as its value of abs(q)/m is too far from every known particle).

An other solution would be to change the threshold .5 for a smaller value, but

  • it would make the game a lot harder because a better precision on the computed radius would be needed,
  • it would not be backward compatible for the test/validator.

What do you think?