# What should be 'the next time'?

A question was asked in a mental ability test (which ended on Saturday).

What comes next in this pattern of time:
2:25, 4:34, 1:57, 6:16, ___

Note:
1. No extra information is given like 12/24 hour time, digital or analog watch, etc.

My approach :

"draw the time" as seen in an analog watch and calculate the angles...

• Is the mental ability test a still ongoing competition? If so, please also read this site policy – BmyGuest Jun 14 '16 at 18:32
• @BmyGuest No, I know the ethical nature of Stack Exchange. The contest ended on Saturday. I felt like sharing the questions :) – ABcDexter Jun 15 '16 at 2:23

5:17

@Aggie Kidd found the last digit (thanks to him also for \rightarrows) and helped me find the others. A friend helped for the first digit :

2:25 $\rightarrow$ $2 + 2 = 4$ $\rightarrow$ 4:34.
4:34 $\rightarrow$ $4 - 3 = 1$ $\rightarrow$ 1:57.
1:57 $\rightarrow$ $1 + 5 = 6$ $\rightarrow$ 6:16.
6:16 $\rightarrow$ $6 - 1 = 5$ $\rightarrow$ 5:?7.

The second digit is:

2:25 $\rightarrow$ $(2 + 2 + 5) \mod 6 = 3$ $\rightarrow$ 4:34.
4:34 $\rightarrow$ $(4 + 3 + 4) \mod 6 = 5$ $\rightarrow$ 1:57.
1:57 $\rightarrow$ $(1 + 5 + 7) \mod 6 = 1$ $\rightarrow$ 6:16.
6:16 $\rightarrow$ $(6 + 1 + 6) \mod 6 = 1$ $\rightarrow$ 5:17.

• Great, that's a good mathematical explanation. I'll crosscheck and reply if this was an option based question. – ABcDexter Jun 15 '16 at 10:30

Given the approach of the OP...

and calculating all the angles on the watch (where one minute is equal to 6 degrees) I came to following values:

 2:25 -> ~78°  4:34 -> ~66°   1:57 -> ~78°   6:16 -> ~90°
Given this pattern I assume the next step would be -12° again, which would make it 78°

Consindering the answer of Aggie Kidd where the last number of the next time has to be a "7", there are 6 possible "minute positions" (7, 17, 27, 37, 47 and 57).

A time like ?:07 is not possible, since the hour hand (hope this is the right word.. I'm a non native English speaker) had to be 13 spaces behind the minute hand (which would make it point one space behind the 11 hour mark).

Same is for ?:17, ?:27, ?:37, and ?:47 since the hour hand is so close to the next hour mark that it can only be ?:57

So my answer is 8:57 which is the only position where the hands are in a 78° angle! (might be way off though :P)

• Yes, "hour hand" is correct English. – Jasen Jun 15 '16 at 10:18
• Finally,, a fellow puzzler with same answer. Yes, this was exactly my answer :) – ABcDexter Jun 15 '16 at 10:25
• Nice to hear that @ABcDexter. I wasn't sure about my answer after I posted this, because I'm still not 100% sold on the pattern :D – Radhato Jun 15 '16 at 10:31

2:25 $\rightarrow$ $2 + 2 = 4$ $\rightarrow$ 4:34.
4:34 $\rightarrow$ $4 + 3 = 7$ $\rightarrow$ 1:57.
1:57 $\rightarrow$ $1 + 5 = 6$ $\rightarrow$ 6:16.
6:16 $\rightarrow$ $6 + 1 = 7$ $\rightarrow$ ?:?7.