Numbers Puzzles

27. If I had one more sister I would have twice as many sisters as brothers. If I had one more brother I would have the same number of each. How many brothers and sisters have I?
Three sisters and two brothers.
This can be solved by simple deduction, but if algebra is used let x be the number of sisters and y the number of brothers :
x+ 1= 2y
y+ 1= x
Therefore, y + 1+ 1= 2y
so y =2 or x + 1= 2x - 2
so x = 3.
28. A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?
The first 56 balls could be of all colours except red. This would leave 8 balls, all of which are red. so any three chosen would be red.