Reply To: The Riddle Thread….

Dr. Pepper-

I was able to solve the first three questions thru two similar brute-force methods.

Each box represents a game (best-of-seven), each marble represents a Philly win (four wins).

Each box must be empty or contain one marble.

We need to figure out all possible combinations of empty boxes and boxes with a marble in them.

The first method is to start with the seven boxes lined up from left to right, and the four marbles in the leftmost boxes.

Each turn will move the rightmost marble one box to its right.

XXXX---

XXX-X--

XXX--X-

XXX---X

XX-XX--

XX-X-X-

XX-X--X

XX--XX-

XX--X-X

XX---XX

X-XXX--

.

The second method is to count using binary numbers with seven on-off switches like so:

X

X-

XX

----X--

----X-X

----XX-

----XXX

---X---

---X--X

---X-X-

---X-XX

---XX--

---XX-X

---XXX-

---XXXX

We will be able to count to 127 using this method.

At this point, the results of the first and second methods will be the same.

It will now be quite clear if one bettor or the other has better odds.

[if either] actually has better odds, just in case anyone else wants to work it out.)

a) Is there a more elegant way of solving this?

b) Is there an equation that will do so?