Random Puzzles 

Workings

Answer
375 children: 70 mothers and 55 fathers.

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
There are fewer than 1,000 apples.

Answer
946 apples.

Reasoning
We know that (answer − 1) is divisible by 3, 5, 7, and 9.

If it's divisible by 9 then it's automatically divisible by 3.

So the number must be a multiple of 5, 7, and 9.

   [5 x 7 x 9 = 315]

Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+ 1).

Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73, and this doesn't work.

Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36, and this doesn't work.

Let's try 3 x 315 + 1: 946 ÷ 11 = 86, and this works, and is the answer.

Workings

Hint
What can digit 4 be?

Answer
6849.

Reasoning
Digit 4 must be a multiple of 3:
   ---3
   ---6
   ---9

Digit 3 is one more than Digit 9 ÷ 3:
   --23
   --36
   --49

Digit 2 is twice Digit 3:
   -423
   -636
   -849

But Digit 4 is one more than Digit 2, which only leaves:
   -849

And Digit 1 is three smaller than Digit 4:
   6849.