Quandaries
and Queries 

thanks in advance. dorothy was going to see the wizard of oz...she stopped at the bakery and bought a box of cookies. she met the scarecrow and gave him half the cookies. she ate half of the remaining cookies and threw one half cookie away. she met the tin man and gave him half the cookies. she ate half the remaining cookies and threw one half cookie away. she met the lion. she gave him half of her cookies. she ate half the remaining cookies and threw the LAST half cookie away. how many cookies did dorothy leave the bakery with? 

Hi Ken, I tell my students that this is a "working backwards" problem. You start at the end and work backwards. I find it helpful to construct a table.
Now you can see why it is "working backwards". The one number you know is in the last row. At that time she had 1 cookie. She ate half of it and threw the other half away.
Now you can complete the nexttothelast row. She gave the lion half the cookies ansd was left with 1, so she must have had 2 cookies at that time.
Now the row before that. Before she threw away half a cookie she had 2 and a half cookies. This was after she ate half the cookies. Thus she must have had 5 cookies.
Using this procedure you can complete the first three rows. Once you have row 1 you can check by going forward. Cheers,Penny 

