Random Puzzles 

Workings

Hint
There are at least 4 answers that fit the question.

Answer
A hole or a vacuum, or perhaps a set of scales, or maybe a shadow.

Workings

Hints
The first letters of the words are: C, N, D, M, S, S, Y, P, P, H, C, A, P, B.

Answers
-----rue = construe -----jar = nightjar -----dil = daffodil -----any = mahogany or epiphany -----pox = smallpox -----gth = strength -----elf = yourself -----oia = paranoia -----ige = prestige -----hog = hedgehog -----too = cockatoo -----dix = appendix -----fin = paraffin -----upt = bankrupt

Workings

Answer
23.

Reasoning
By likely, we mean greater than 50% chance.

With one person there is a 0 percent chance that you'll have two people with the same birthday.

With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).

With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).

Notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.

We keep adding people until the %age is greater than 50%.

When we have 23 people the %age is 50.729%.

Workings

Hint
The 4^th word begins with the letter Q.

Answers
ba-g- = badge (DE) d--ed = dazed (AZ) dia-- = diary (RY) -uo-a = quota (QT) i-de- = index (NX) -o-el = vowel (VW) -um-s = bumps (BP) py--y = pygmy (GM) g-ou- = ghoul (HL) --nal = final (FI) tra-- = track (CK) -umb- = jumbo (JO) d--ty = dusty (US)
This puzzle isn't guaranteed to have a unique answer, can you find another?