Random Puzzles 

Workings

Hint
One possibility answer might be associated with an apiary.

Answer
Common words: beekeeper, beekeepers, beekeeping, freebee, freebees, freewheel, freewheeled, freewheeling, freewheels, peewee, peewees, reengineer, reengineered, reengineering, reengineers, squeegee, squeegeed, squeegeeing, squeegees, teepee, teepees.

All words: beebee, beebees, beekeeper, beekeepers, beekeeping, beekeepings, beetleweed, beetleweeds, cheekteeth, deepfreeze, deepfreezes, deepfreezing, deerweed, deerweeds, freebee, freebees, freesheet, freesheets, freewheel, freewheeled, freewheeler, freewheelers, freewheeling, freewheelingly, freewheelings, freewheels, geechee, geechees, greegree, greegrees, greenkeeper, greenkeepers, greenleek, greenskeeper, greenskeepers, greenweed, greenweeds, leechee, leechees, peebeen, peebeens, peesweep, peesweeps, peetweet, peetweets, peewee, peewees, preengineered, reengineer, reengineered, reengineering, reengineers, sleeveen, sleeveens, sneezeweed, sneezeweeds, squeegee, squeegeed, squeegeeing, squeegees, streetkeeper, streetkeepers, teepee, teepees, teetee, treecreeper, treecreepers, tweedledee, tweedledeed, tweedledeeing, tweedledees, veepee, veepees, weewee, weeweed, weeweeing, weewees.

Workings

Hint
Mary's name is Dancer.

Answer
Louise Archer will make the chocolate cake.
Julie Bowness will make the coffee cake.
Kay Cook will make the plain cake.
Mary Dancer will make the vanilla cake.

Workings

Hint

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 first letters of the words are: T, C, K, F, D.

Answers
finger[tip]toe   copy[cat]walk    don[key]hole    out[fox]trot  every[day]dream