Pascal’s Pizza

Mary Claire brings home a puzzle to solve for her Focus class each week. Sometimes she asks me for help. I enjoy trying to guide her to figuring it out herself.

This week’s problem was how many pizza combinations can you make using zero to five different toppings: sausage, mushrooms, pepperoni, peppers, and onions. Mary Claire set up a grid and made X’s next to each ingredient to come up with all combinations. She discovered this pattern:

1 that is plain

5 that have 1 topping

10 that have 2 toppings

10 that have 3 toppings

5 that have 4 toppings

1 that has 5 toppings

She added them up for the answer, 32. Danny noticed the pattern and said, “That’s Pascal’s triangle.” He drew the triangle. See: All You Ever Wanted to Know About Pascal’s Triangle and more.

Mary Claire recognized the triangle of numbers and said she recognized it. In her class they called it the Period of Mystery. I asked her, “Why do you think they call it period?” She said, “Because it is shaped like a period.” I then realized her mistake. “You mean, Pyramid of Mystery.” She agreed that name made more sense, given that Pascal’s Triangle looks more like a Pyramid that a period.

I just want to know when did they start teaching third graders about Pascal’s Triangle?

Now playing: Don’t Lose My Number by Phil Collins

Bullfrog Relocation

BullFrog3.jpgOur little pond has been the home to several frogs over the years. Our first giant bullfrog died one winter when the pond partially froze. A smaller bullfrog survived and grew to the size of my fist. He had a very deep “croak.” One reason he grew quickly is that he would sit under the pond lights and lick bugs out of the air. Cherry picking, so to speak.

We’ve had goldfish disappear over the years, and we suspect that as the bullfrogs got large enough, they decided to cherry pick fish. Kathy and I decided to evict giant bullfrogs from now on.

Using a net and the cloak of darkness, it took me four nights to catch the giant bullfrog. He would jump just before my net could grab him. I even had a rimshot one time, as he bounced off the lip of the net. I noticed a pattern in his jumping… always jumping into the water in the back corner of the pond. So last night I approached the frog slowly, making sure the fountain spray interfered with his line of sight. With the net hiding behind the front pond wall, I quickly rushed forward, placing the net in the anticipated jump target. He didn’t move! I think the spray-block really helped with the element of surprise. I slowly moved the net toward Mr. Bullfrog, and he suddenly jumped right into the net. Victory!

Clyde had been watching with excitement from the kitchen window. I decided to bring my catch into the house to show Kathy. As I came up on the deck, Mr. Bullfrog (who had been trying to jump out of the net) found good footing and jumped out. He landed on the deck, and with one leap, jumped into the darkness of the backyard.

I ran inside to get a flashlight with net still in hand. Clyde ran with me to the basement and then back outside to track down the frog. He was very excited and glad to help. I was able to point the flashlight and Clyde in the right direction, and he tracked down the frog quickly. The frog hopped once, but I was able to snatch him with the net, trapping him on the walkway. Clyde stood over the frog sniffing. He was very excited.

BullFrog2.jpgKathy came out and helped us get the frog into a cooler so we could deport him to a nearby pond. I took him up in the shower so I could take a few pictures and not worry about him jumping away. Clyde stood guard watching through the shower door glass.

At 9:45 pm the three of us (Kathy, Clyde, and myself) loaded the frog in the car, and went to pick up Kelly from Rachel’s and Mary Claire from a birthday party. We all decided to take the bullfrog to a very nice pond in the back of a model home in a new subdivision. He’s now sitting happily under the built-in waterfall. The pond has spotlights which will attract bugs and allow him to continue cherry picking. When the model home is purchased, the new owners will have a bonus of a croaking bullfrog. Hope they don’t buy any goldfish.

Now playing: Come On Up To The House by Tom Waits