Funny math problem to calculate the Pin Number for a credit card.

08102021, 05:31 AM
(This post was last modified: 08102021 05:43 AM by Steve Simpkin.)
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Funny math problem to calculate the Pin Number for a credit card.  
08102021, 05:34 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.  
08102021, 05:41 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.  
08112021, 03:40 PM
(This post was last modified: 08122021 10:45 AM by Albert Chan.)
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RE: Funny math problem to calculate the Pin Number for a credit card.
(08102021 05:41 AM)Steve Simpkin Wrote: Here is the solution using a Casio fx991EX. FYI, integrand singularity (at x=1) is removable. (3x^3x^2+2x4) / √(x^23x+2) = (x1)*(3*x^2+2*x+4) / √((x1)*(x2)) = (1x)*(3*x^2+2*x+4) / √((1x)*(2x)) // integral limits 0 to 1, √(1x), √(2x) both real = (3*x^2+2*x+4) * √(11/(2x)) XCAS> ∫((3*x^2+2*x+4) * √(11/(2x)), x=0..1) (202*sqrt(2) + 135*ln(2*sqrt(2)+3))/16 // ≈ 2.98126694401  Proof: assume integral have the form f*√g (f*√g)' = f'*√g + f/(2√g)*g' = (f'*g + f*g'/2) / √g XCAS> f := a*x^2+b*x+c // integrand numerator is cubic, thus quadratic f XCAS> g := x^2  3x + 2 // integrand denominator = √g XCAS> coefs := e2r(f'*g + f*g'/2) [3*a, (15*a+4*b)/2, (8*a9*b+2*c)/2, (4*b3*c)/2] Ignore constant term for now, we match 3 coefs with 3 unknown. XCAS> a, b, c := 1, 13/4, 101/8 XCAS> coefs [3, 1, 2, 199/16] // = [3, 1, 2, 4]  [0, 0, 0, 135/16] I1 = preval(f*√g, 0, 1) = subst(f*√g, x=0) = 101/8*√(2) I2 = ∫(1/√(x^23x+2), x=0..1) // let y = 2*(x3/2)=2x3, dy = 2 dx = ∫(1/√(y^21), y=3 .. 1) // ∫(1/√(y^21), y) = ln(abs(y+sqrt(y^21))) = ln(2*√(2)+3) I = I1 + 135/16 * I2 = 101/8*√(2) + 135/16*ln(2*√(2)+3) 

08122021, 07:54 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.
You never cease to amaze me, Albert!
Took me only three reads to understand this time ;) Nice trick. Cheers, Werner 

08122021, 03:05 PM
(This post was last modified: 08122021 03:52 PM by Albert Chan.)
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RE: Funny math problem to calculate the Pin Number for a credit card.
(08112021 03:40 PM)Albert Chan Wrote: I2 = ∫(1/√(x^23x+2), x=0..1) // let y = 2*(x3/2)=2x3, dy = 2 dx Another way is to map y=2*x3 for the full integral, then solve by integration by parts Note that above quoted expression, map from x to y, numerator of 1 stayed 1. XCAS> e2r(r2e([3,1,2,4], (y+3)/2), y) → [3/8, 25/8, 77/8, 55/8] I = ∫((3y^3 + 25y^2 + 77y + 55) / √(y^21), y=3 .. 1) / 8 Y0 = ∫(1/√(y^21),y) = ln(abs(y+√(y^21))) Y1 = ∫(y/√(y^21),y) = ∫d(√(y^21)) = √(y^21) Y2 = ∫(y^2/√(y^21),y) = ∫(y*d(Y1)) = y*Y1  (Y2Y0) 2*Y2 = y*Y1 + Y0 Y3 = ∫(y^3/√(y^21),y) = ∫(y^2*d(Y1)) = y^2*Y1  2*(Y3Y1) 3*Y3 = (y^2+2)*Y1 3*Y3 + 25*Y2 + 77*Y1 + 55*Y0 = (y^2+2)*Y1 + 25/2*(y*Y1+Y0) + 77*Y1 + 55*Y0 = (y^2+25/2*y+79)*Y1 + 135/2*Y0 I = preval((y^2+25/2*y+79)*√(y^21) + 135/2*(ln(abs(y+√(y^21)))), 3, 1, y) / 8 = 101/8*√(2) + 135/16*ln(2*√(2)+3) ≈ 2.98126694401 

08122021, 11:41 PM
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RE: Funny math problem to calculate the Pin Number for a credit card.
I guess I just don't see the point. A credit card that requres a PIN number either comes with a preassigned PIN or lets you choose the PIN; most of mine let you choose. A calculated PIN would seem unnecessary in both cases.


08132021, 12:02 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.
(08122021 11:41 PM)Don Shepherd Wrote: I guess I just don't see the point. A credit card that requres a PIN number either comes with a preassigned PIN or lets you choose the PIN; most of mine let you choose. A calculated PIN would seem unnecessary in both cases. I think the humor here is that the person writing the letter and being generous with their credit card (probably uncharacteristically for them) assumes their partner will not be able to solve the math problem and get the PIN number (probably 2981). I showed this to my wife and she laughed and then said "Ass". 

08132021, 05:30 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.
Solve on the HP15C gives pretty much the same value for the integral between 0 and 0.99999.


08132021, 07:52 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.
Hi,
Could someone test it on a real HP42S ? Because I've just tested in its swiss clone and I don't get error with [0, 1] boundaries ;)  HP 48GX, Prime G2, 50G. A long time ago : 11C, 15C, 28C, 28S. SwissMicros DM42, DM15L 

08132021, 08:57 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.
It is wellknown that the numerical integration in, I think, all its HP implementations (from 34C onwards) never evaluates the endpoints. Free42 and, by extension, the DM42 are such faithful simulators that they of course mimic that, too.
But I did try it out on a real 42S of course. No problem whatsoever. Code: 00 { 41Byte Prgm } With ACC= 0.0001 I get 2.98125065973 Cheers, Werner 

08132021, 05:26 PM
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RE: Funny math problem to calculate the Pin Number for a credit card.
(08122021 03:05 PM)Albert Chan Wrote: I = ∫((3y^3 + 25y^2 + 77y + 55) / √(y^21), y=3 .. 1) / 8 Another way, by regroup terms. (odd and even powers of y) diff(y*√(y^21), y) = (2*y^21) / √(y^21)) I = ∫((3/8*(y^21)+10)*y/√(y^21), y=3 .. 1) + ∫((25/16*(2*y^21)+135/16)/√(y^21), y=3 .. 1) For first term, let z = y^21, dz = 2y dy: ∫((3/8*(y^21)+10)*y/√(y^21), y) = ∫(3/16*√z+5/√z, z) = 1/8*z^(3/2) + 10*√z I = preval((z/8+10)*√z,8,0,z) + preval(25/16*(y*√(y^21)) + 135/16*(ln(abs(y+√(y^21)))),3,1,y) = 22*√(2) + (150*√(2)+135*ln(2*√(2)+3))/16 = 101/8*√(2) + 135/16*ln(2*√(2)+3) 

08132021, 08:00 PM
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RE: Funny math problem to calculate the Pin Number for a credit card.
(08102021 05:31 AM)Steve Simpkin Wrote: This cute math problem to calculate the Pin Number for a credit card popped up on a post in the Facebook HP Calculator Fan Club group recently. Apologies if it has been posted before. I see an answer with a lot of decimals but what's the PIN? Tom L Cui bono? 

08182021, 12:19 AM
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RE: Funny math problem to calculate the Pin Number for a credit card.  
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