# What are the missing patterns? (From a 5th grader's school book)

This is a photo of a puzzle my facebook friend took, supposedly from a 5th grader's school book. For both puzzles the bottom row with two patterns is missing. The puzzle "a" is fairly simple one, but I don't think many 5th graders (so 10-11 years olds) could get the "b" right (or then the real solution is simpler than I think!).

What's the solution to the puzzle B?

Bonus: can you get a 10-11 year old to solve this? :-) A shape like the top left example, but with a "roof" and a shape like the left middle which has a thick horizontal line across the middle. Each test has 3 different variables to the patterns which come in 2 varieties for 2^3=8 different shapes. After identifying the 3 varying factors (roof/no roof, diagonal/vertical line, thick/thin horizontal line), you can find the missing permutations.

I'm not sure how difficult that would really be for a 5th grader. It's not as simple as A somehow, but only because the variations are more complex to recognize and count. I'm not sure why though.

• Corrected, sorry – RobStone Aug 19 '16 at 7:29
• I get your reasoning for the missing two patterns, but what determines which is left and which is right? – JanneK Aug 19 '16 at 7:51
• The left and right columns of three shapes each displayed as examples for problem b – RobStone Aug 19 '16 at 7:52
• The order is arbitrary. I just picked the two examples that matched 2/3 of the factors and named the 3rd which needed to be changed for each to finish the set. – RobStone Aug 19 '16 at 8:01
• Hmmm... I do like Rosie's answer better as well. It seemed to bother me that I couldn't define a "sequence", so I simply identified the missing permutations and ignored the pattern of how they should fit. As patterns go, her answer is more correct. – RobStone Aug 19 '16 at 8:38

Some thoughts:

a: Overall shape: two shapes that are two vertical spaces apart are round and a square. So round then square. Middle blob: solid circle then hollow circle. Other line: at right-angles to what it is in neighbouring pictures. So horizontal then vertical.
To summarise: a: Left: Round overall shape, solid circle inside, horizontal line. Right: Square overall shape, hollow circle inside, vertical line.
b: Roof: two shapes that are two vertical spaces apart are one with and one without a roof. So roof then no roof. This is, incidentally, the only sequence we haven't had so far -- a principle which can be applied to the other variables. Horizontal: thick then thin as that's the only sequence we haven't had so far? Vertical or slant: Vertical then slant as that's the only sequence we haven't had so far?
To summarise: Left: roof, thick, vertical. Right: no roof, thin, slant.

• This is the solution I came up with. According to the kid, @RobStone's answer is right, though I think this is a correct one as well (and only has one valid solution, whereas the other one has two). I'll mark RobStone's answer as the correct one as he was the first to come up with a valid solution, altough I don't think this is a lesser one! :-) – JanneK Aug 19 '16 at 8:11