By: Thad Beier

Thad Beier — Fri, 12 Jun 2009 23:47:00 +0000

I noticed that the solutions are a factor of 5.8284 (sqrt(2) + 1)^2 apart. So, using the “don’t try this” method of adding one to T or B actually works if you can get a good guess for the start. Values for T are 21, 120, 697, 4060, 23661, …

By: Doug Jenkins

Doug Jenkins — Mon, 11 May 2009 08:10:00 +0000

Michael - very neat. At first I couldn't see why precision would be a problem, but a quick trial verified that it was. I then set up a brute force solution using the decimal data type, which gives 28 significant figures, but is way too slow unless you know the answer already.

FWIW, here is the code using decimals:

Function P_100(Min_discs As Double) As Variant
Dim B As Variant, n As Variant, Prob As Variant, ans(1 To 3, 1 To 1) As Double
Dim b_2 As Variant, n_2 As Variant, Remain As Variant

ans(3, 1) = Timer
n = Min_discs - 1
Do
n = CDec(Int(n + 1))
B = CDec(Int(n * 0.5 ^ 0.5) - 1)

Do
B = B + 1
Prob = ((B / n) * ((B - 1) / (n - 1)))
Loop While Prob - 0.5 .LT. 0
b_2 = CDec(B * (B - 1))
n_2 = CDec(n * (n - 1))
Remain = n_2 - (2 * b_2)
Loop While Abs(Remain) .GT. 0

ans(1, 1) = B
ans(2, 1) = n
ans(3, 1) = Timer - ans(3, 1)
P_100 = ans

End Function

Comments on: Euler Problem 100

By: Thad Beier

By: Doug Jenkins