Random Puzzles 

Workings

Hint
Look at the first and third columns first.

Answer
The missing sum is 40.
Circle   = 12
Star     = 3
Square   = 7
Triangle = 9

Reasoning
Looking at Column 1 and Column 3 we have:

[1]   Square + Star + Circle + Square = 29
[2]   Square + Square + Triangle + Star = 26

If we subtract [1] − [2] we get:

[3]   Circle − Triangle = 3

And Row 3 is:

[4]   Circle + Circle + Triangle + Circle = 45

If we add [3] + [4] we get:

Circle + Circle + Circle + Circle = 48

So, Circle = 12.

Using [3] we find that Triangle = 9.

Using Column 2 we find that Star = 3.

Using Row 1 we find that Square = 7.

Double-Checking
The rows add to: 35 + 26 + 45 + 25 = 131.

The columns add to: 29 + 36 + 26 + 40 = 131.

The rows and columns must add to the same number, so this could have been used a shortcut to the missing sum.

In total, there are:
   5 Squares   = 5 x 7  = 35
   5 Circles   = 5 x 12 = 60
   3 Stars     = 3 x 3  =  9
   3 Triangles = 3 x 9  = 27

Which is also a total of 131.

So all of the totals are the same, as expected.

Workings

Hint
The word starts with the letter Q.

Answer
Queue.

Less common words: aqueous, gooiest, obsequious, onomatopoeia, plateaued, plateauing, queued, queueing, queues, sequoia, sequoias, subaqueous.

All words: aqueous, archaeoastronomer, archaeoastronomers, archaeoastronomical, archaeoastronomies, archaeoastronomy, assegaaied, assegaaiing, banlieue, banlieues, beauish, blooie, camaieu, camaieux, cooee, cooeed, cooeeing, cooees, dequeue, dequeued, dequeues, enqueue, enqueued, enqueues, epigaeous, epopoeia, epopoeias, euoi, euois, euouae, euouaes, flooie, forhooie, forhooied, forhooieing, forhooies, giaour, giaours, gooier, gooiest, guaiac, guaiacol, guaiacols, guaiacs, guaiacum, guaiacums, guaiocum, guaiocums, hawaiians, homoiousian, homoiousians, hypoaeolian, hypogaeous, loaiasis, looie, looies, louie, louies, maieutic, maieutical, maieutics, meoued, meouing, metasequoia, metasequoias, miaou, miaoued, miaouing, miaous, mythopoeia, mythopoeias, nonaqueous, obloquious, obsequious, obsequiously, obsequiousness, obsequiousnesses, onomatopoeia, onomatopoeias, palaeoanthropic, palaeoanthropological, palaeoanthropologies, palaeoanthropologist, palaeoanthropologists, palaeoanthropology, palaeoecologic, palaeoecological, palaeoecologies, palaeoecologist, palaeoecologists, palaeoecology, palaeoenvironment, palaeoenvironmental, palaeoenvironments, palaeoethnologic, palaeoethnological, palaeoethnologies, palaeoethnologist, palaeoethnologists, palaeoethnology, palaeoichthyologic, palaeoichthyological, palaeoichthyologies, palaeoichthyologist, palaeoichthyologists, palaeoichthyology, pharmacopoeia, pharmacopoeial, pharmacopoeian, pharmacopoeias, plateaued, plateauing, prosopopoeia, prosopopoeial, prosopopoeias, queue, queued, queueing, queueings, queuer, queuers, queues, queuing, queuings, radioautograph, radioautographic, radioautographies, radioautographs, radioautography, radioiodine, radioiodines, reliquiae, rhythmopoeia, rhythmopoeias, saouari, saouaris, scarabaeoid, scarabaeoids, sequoia, sequoias, subaqueous, tenuious, terraqueous, toeier, toeiest, zoaea, zoeae, zooea, zooeae, zooeal, zooeas, zoogloeae, zoogloeoid, zooier, zooiest.

Workings

Answer
 

Workings

Hint
Think outside the box.

Answer
Start from the top left dot, and go past the top right dot, and then diagonally down to the bottom left dot, back up to the top left dot, and diagonally down to the bottom right dot.