A couple travelling across South Australia bought a bag of oranges. You are not allowed to carry fruit or veggies across the border to Western Australia. As they approached the border a man stepped out and asked if they had any fruit. They confessed that they did.The man said that he would let them go if they gave him half of their oranges and half an orange. They did this.
Further along the road a woman stepped out and stopped them. She made the same request, half of your oranges and half an orange. They did this.
At the border the customs man made the same request, half of your oranges and half an orange.
This meant that they could then cross the border as they had NO oranges left.
How many oranges did they have to start with?
Answers later.
Den.

THis is an easy problem if you start from the end. the equation is-:
2x+1=y. where X is the number of oranges left.
Den.


If X=0 then 2x0=0 0+1=1 ½ of their oranges + ½ an orange = 1

One step back. If X=1 then 2x1=2 2+1=3 Half of 3 is 1½ plus ½ =2
next step back, If X=2 then 2x2=4 4+1=5 Half of 5 is 2½ plus ½ =3
next step back, If X=3 then 2x3=6 6+1=7 Half of 7 is 3½ plus ½ =4

So they started with 7 and ended up with none and no oranges cut up.
Q.E.D.
Den.

Very mathematical as an answer! When I first looked at this I got into really deep water with your half an orange. Seemed to me that eg. if there were 10 oranges to start with, then half the oranges would be five .. plus half an orange = five and a half oranges. So the couple would be left with four and a half oranges. Then for the next request they would have to give her half their oranges .. half of four and a half is two and a quarter .. then plus half an orange would be two and three quarters .. leaving them with one and three quarters of an orange.

This was getting very messy! So I gave up on it.

But then later, I realised that the essence of this is to have an odd number of oranges. Then it doesn't become so messy! Eg. 11 oranges. Half of that would be five and a half .. plus half an orange makes six (which they give him). They would then be left with five oranges (another odd number). Again, half of five would be two and a half .. plus half an orange = three oranges which they give her, leaving them with two. Then it gets messy again as you're down to an even number.

But I can see how 7 would work.

First request. Half of seven = three and a half .. plus half an orange = four oranges .. which they give him, leaving them with three oranges.

Second request. Half of three = one and a half .. plus half an orange = two oranges .. which they give to her, leaving them with one orange.

Third request. Half of their one orange = half an orange .. plus half an orange = one orange .. which they give to him.

So they have no oranges left and are therefore allowed to cross the border.

Hugh