# Roulette pattern

Mary was playing bingo when she noticed a logical sequence in the numbers of the balls as they came out. The numbers of the balls, in the order they came out, are shown below.

55, 52, 51, 48, 47

If the ball numbers were actually following a pattern, what would the next ball number be?

A) 46
B) 44
C) 39
D) 43

My problem is that I have no context for this puzzle. So I believe that the context is relevant to determine what the next ball number will be. Considering that they are taken cyclically, the next number would be... 44?

• rot13(V oryvrir lbh zrna 44. Naq lrf gung frrz gb or gur nafjre.) Nov 15 '20 at 21:24
• @Prim3numbah rot13 is a common way to post a comment that may contain spoilers. You can encrypt/decrypt rot13 here. Nov 16 '20 at 1:57
• Bubbler, I think you meant @gmn_1450. Prim3numbah already used rot13. Nov 16 '20 at 2:00
• Oops, sorry. My mistake. Nov 16 '20 at 2:12
• @gmn_1450 It's cyclic like you say and the difference between to adjacent numbers alternates between -3 and -1. So last should be 47 - 3 which is option B 44 Nov 16 '20 at 9:44

It seems like the most likely answer to this question is

B) 44

Because

This is a list of numbers $$n$$, in decreasing order, such that either $$n$$ or $$n+1$$ is divisible by $$4$$.

With a recursive relationship, you may be able to convince yourself that the answer is

A) 46

Reasoning

If $$a_n$$ represent the elements of the sequence then $$a_{n+1} = \begin{cases} a_n - 3, & \text{if the product of the digits of}\ a_n \text{ is odd} \\ a_n - 1, & \text{otherwise} \end{cases}$$

Or perhaps with a little more maths (and the help of the OEIS) you may convince yourself that the answer is

D) 43

Because

If $$p_k$$ represents the $$k$$th prime number, then these are the numbers $$n$$ such that $$p_n^2 - 2$$ is a prime, in decreasing order.