Occasional Puzzles - Adventures in Puzzlevania
Today’s Puzzle
In the magical land of Puzzlevania, you are on your way to visit your friend Theo for his 10th birthday. As is tradition in Puzzlevania, you want to bring him two cakes. You must cross seven bridges to get to his house and, unfortunately, each bridge has a troll under it.
Trolls in Puzzlevania are mean but not, like, super mean. Before each bridge crossing, the resident troll will take half of your cakes. But immediately after the crossing, he will feel bad and give you one cake back.
How many cakes do you need to start out with in order to arrive at Theo’s house with exactly two?
(Note that trolls do not accept half-cakes. If, at any time, you have an odd number of cakes, you will lose an extra half-cake. For example, if you come to a bridge with 9 cakes, the troll will take 5 of them before the crossing, not 4.5.)
Friday’s Puzzle - Give this one a tri
Ten circles are arranged in a triangle, as above. Turn the triangle upside down by moving just three of the circles (and no, just turning your computer screen upside down doesn’t count!).
[SPOILER] Answer to Friday’s Puzzle
There’s a couple of ways you can think about this. One is to rotate the three corners of the triangle like so:
The other is to “flip” the triangle by moving the bottom corners up and moving the tip to the other side:
(Technically, since there are three circles moving to three new positions, there are six ways to do it (3! = 3*2*1 = 6), and any one of them is correct!)