## BOYS AND GIRLS.

(

Moving Counter Problem)

If you mark off ten divisions on a sheet of paper to represent the

chairs, and use eight numbered counters for the children, you will have

a fascinating pastime. Let the odd numbers represent boys and even

numbers girls, or you can use counters of two colours, or coins.

The puzzle is to remove two children who are occupying adjoining chairs

and place them in two empty chairs, _making them first change sides_;

then remove a second pair of children from adjoining chairs and place

them in the two now vacant, making them change sides; and so on, until

all the boys are together and all the girls together, with the two

vacant chairs at one end as at present. To solve the puzzle you must do

this in five moves. The two children must always be taken from chairs

that are next to one another; and remember the important point of making

the two children change sides, as this latter is the distinctive feature

of the puzzle. By "change sides" I simply mean that if, for example, you

first move 1 and 2 to the vacant chairs, then the first (the outside)

chair will be occupied by 2 and the second one by 1.

## Answer:

There are a good many different solutions to this puzzle. Any contiguous

pair, except 7-8, may be moved first, and after the first move there are

variations. The following solution shows the position from the start

right through each successive move to the end:--

. . 1 2 3 4 5 6 7 8

4 3 1 2 . . 5 6 7 8

4 3 1 2 7 6 5 . . 8

4 3 1 2 7 . . 5 6 8

4 . . 2 7 1 3 5 6 8

4 8 6 2 7 1 3 5 . .