ABBA Gold is a series of nineteen puzzles, plus a bonus, inspired by the song titles on ABBA's best-selling album, "Gold: Greatest Hits". The caches form a circuit of roughly five miles, on some pleasant footpaths around Pirbright. Be prepared for wet and muddy conditions!
See ABBA Gold (the bonus puzzle cache) for an overview of the series.
ABBA Gold #03: Take A Chance On Me
Gotta put me to the test…
The probability of rolling a 1 on any one of these 'loaded' dice is p(1), the probability of rolling a 2 is p(2), and so on.
The cache can be found at:
N51° 17. [ p(4)/p(3) ] [ p(2)/p(6) ] [ 3*p(5)/p(1) ]
W0° 39. [ p(3)/p(6) ] [ 24*p(1)/p(5) ] [ 4*p(4)/p(2) ]
Hints for non-mathematicians:
- Consider the number of ways in which you can reach each total. For example, there is only one way to get a total of 3, but three ways to get 4, and six ways to get 5.
- The probabilities of each individual score on a single die, from p(1) to p(6), sum to one.
- The probability of any single combination is the product of the probabilities for the three dice. So, to roll a 1 with the first die, a 2 with the second, and a 4 with the third, the probability is p(1) * p(2) * p(4).
- Work from the the lowest total upwards.
- The easiest way to do this is to use a spreadsheet to work out all the possible totals and the way to get them.
FTF honours to ===sgb. Congratulations!