Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Have You Got It?

Can you explain the strategy for winning this game with any target?

Stage: 3 Challenge Level:

What are the factors of $711$?

If you have four numbers whose product is $7.11$, you can double one of the numbers and halve one of the others, and the product will still be $7.11$,

or

you can double one of the numbers, treble another and divide a third by six, and the product will still be $7.11$,

or...

What else can you do that leaves the product unchanged?

This is quite a challenging problem. If you get part of the way and would like more hints, try posting a question on the Please Explain section of the AskNRICH web board.