The Math and Science of Last Bites

I know, math, or anything involving math or science, on Mondays or, as some of you have let me know in comments, math on any day, is not welcome here. Well, Maddie begs (literally) to differ. On behalf of dogs everywhere, she would like to explain the math and other such rules regarding last bites – as in “you can have the last bite” of toast or cookies or a sandwich.  These are observations, in no particular order.

Note: This is an additional item. The original post was scheduled before Linda G. Hill’s JusJoJan prompt, but since one of the photos in the gallery includes Smokey’s fingertips, I’m adding this to her challenge.

Crumbs resulting from the eating process are to be dumped into the dog’s bowl but cannot be substituted for the last bite.

Butter, frosting and dips that the dog enjoys must exist on the last bite in an equal or greater amount as what existed on any previous bite. To make the complex geometry easier, just give the bite with the largest glob of butter to the dog.

Broken items create additional last bite vectors. This is particularly important when you are eating pizzelles. Every individual piece of a pizzelle includes a last bite.

One-bite forfeiture – Pieces of pizzelle, crackers, cookies or perhaps the end cuts of a ham or roast, which are too small to be divided into more than one bite are, by default, the last bite.

Sandwiches are a last bite reducing mechanism. The two pieces of bread, ham, cheese and perhaps bacon (because that’s always a good idea) become one item once assembled. Therefore, preparation treats are important. Particularly from the ham/cheese/bacon group. However, see below.

Last bites multiply when items are divided. If you have two pieces of toast and cut each in half, there will be four last bites. If you cut a sandwich in half, you create two last bites.

Food that is dropped and recovered by the dog does not count toward the last bite, even if it was the last bite that was dropped. In the case that the last bite of a food item is dropped, an additional food item must be opened/prepared in order to secure a proper last bite. Note: The replacement last bite will be the first bite of the additional item and the last bite of that item must still be given to the dog.

Just as samples consumed while shopping at Costco do not contribute to your total cost at checkout, bites offered during preparation are not considered during the last bite calculation. The phrase “you had your bite when I was preparing this…” is irrelevant and not admissible.

Items which cannot be eaten by the dog must be accompanied by items which can be eaten. Milano cookies, for example, cannot be eaten due to the inseparable chocolate layer. Therefore, a plain cookie (which can be divided into a number of pieces equal to the number of Milanos) must accompany the verboten cookie.

Snack food addendum – Food items like Fritos and pretzels which are normally eaten whole, must be shared with the dog on a per-serving basis. If you take a handful of Fritos, the last one in your hand is the dog’s. If you consume the entire bag at one sitting, the last item in the bag also belongs to the dog. If you share the bag with others, the per-serving last bite requirement extends to all parties equally.

Maddie urges all dogs to add any rule that she has not covered, in the comments.


  1. The entire committee of felines in this blogger’s household wish to congratulate Maddie and her outstanding achievement in human training! Well done!

    By the way, the blogger also wishes to express her thanks for the chuckles. Great way to start Monday.

    Liked by 3 people

  2. Pillow is a wonderful role, as is being the provider of delectable foods. Thanks for the tour and update. PS. I love Maddie’s new vest. 🙂

    Liked by 2 people

    • I wouldn’t want to write the rules on feeding squirrels. I think it’s basically – give me all your peanuts. We haven’t had raccoons for a long time, but as I recall, everything leftover, even if it’s “securely” in the trash.

      Liked by 2 people

    • Bobby and Suzie are eating lunch. They each have a sandwich, an apple and two cookies. Bobby cuts his sandwich in half. One of Suzie’s cookies is broken into three pieces. How many bites does Bobby’s dog Max get?

      If it helps, they can all be on a train heading to Chicago at 85 mph (137 kph).

      Actually, if you gave Maddie a bite of your sandwich, she’d give you an ‘A’ :-)

      Liked by 3 people

  3. Can’t stop laughing! Canine math is in a class all its own, and no dog would fail the course. In my lifetime I’ve had many dogs so I have seen this played out over and over. One dog in particular, Tripper, ( because she was always tripping us as a puppy!) had a routine down whereby she not only got the last bite, she wheedled ‘one more’ bite after that!

    As a kid, I was thrilled with this routine because a lot of my unwanted food disappeared under the kitchen table!! 🤗

    Another great moon shot. Chinook is one handsome boy, and Maddie’s new vest looks comfy and toasty warm. The squirrels don’t have to worry about the ‘last bite’, they look well fed.

    4″ of snow for us. Not so bad. Supposed to get sunshine later, so that will help. Trees look beautiful!

    Liked by 2 people

    • I figured you already passed this course, Ginger or that Murphy would be happy to give you lessons.

      Maddie always gets a bite during the preparation phase, but it never takes the place of the last bite.

      We got about 2″. I moved it out of the way. No walk today, since the three houses whose sidewalks I cleared seem to be the only ones that are clean.

      Take care. Enjoy the sun.

      Liked by 1 person

  4. I read your post aloud to assimilate the math better and Gibbs heard me. He’s a little jealous, wondering why he never gets “last bites.” I have some explaining to do.

    Give Maddie a second to last bite today and see how that adds up.

    Liked by 2 people

  5. Now, that’s the way to teach Math, Dan – tasty, appetising and creative. Love the way Smoky (is that his name), makes his appearances in your posts. Also, love Maddie’s new vest.

    Liked by 2 people

    • Thanks Don. Maddie says this is an important area of math that needs to be explored in greater detail.

      We have several black squirrels in the yard. We call them all Smokey. They’re so darn cute.

      Liked by 2 people

  6. Too much math for me, I have a non math brain. And another hot dog bun, really? And all this time I thought you were a nice guy😂 But I think you must have been looking over my shoulder as I put in a grocery order. Along with the essentials this month including TP, detergent, and tylenol, added some Archway cookies and fritos! My bad..

    Liked by 2 people

  7. First things first: If Maddie doesn’t eat the Lotus biscuits, they are mine. Crumbs and all. Second: that is one beautiful full moon photo.
    Parker loves peanut butter. At lunch, when my husband makes his PB&J (every single day), he has to get a spoon and put peanut butter on it just for her. Pumpkin loves to sneak lettuce and radishes when I’m making a salad. Every gal for herself. Piper is ambivalent to the entire process. She has no knowledge of ‘last bite.’ Wonderful post, Dan.

    Liked by 2 people

    • Those cookies are great. You would have to fight Maddie for them, and then me. They have them for ridiculously cheap at Costco, which is where I get the pizzelles I eat. Maddie loves pizzelles, and she keeps a sharp eye on how many pieces they break into.

      I’ve never known a cat that eats peanut butter – that’s funny. Maddie will eat peanut butter on an english muffin (bite) or on celery. We had a cat that would chew lettuce, but never actually eat it.

      Liked by 2 people

      • Back when I was working (gosh, it feels great to say that), I would fly for a conference every August. One time, I was seated next to an older woman who kept eyeing my Lotus biscuit. She asked if I was going to eat it. I told her indeed, I was. Then I told her I buy these at the grocery store, and she was shocked. She thought they were strictly an airline cookie. She told me she couldn’t wait to get home and hit the grocery store!

        Liked by 2 people

    • I did fear the word ‘math’ would send some people fleeing the page, Teagan. I’m glad you stuck around. These might better be called ‘procedures’ but that word scares me more than math.

      Liked by 2 people

  8. Happy smiles from this cute post! Good dog math, fersure. This math did not hurt my brain at all, thank you! Sadie has had 1/4 omelet, brisket and cauliflower and broccoli and will soon have a glob of peanut butter with a soupcon of fish oil garnished with a crunchy allergy med.

    I must say, that looks like a bouncy horse set, and not a merry-go-round?

    Liked by 1 person

    • Haha – no, no, no offense intended. Any resemblance to innocent men is purely coincidental? Maddie used to get mad when I’d have Milan
      No’s, and I’d sit there saying “you can’t have chocolate.”

      Liked by 1 person

  9. I think I should have read this one this morning. That’s an intricate system. Buuuut….our old pal Buddy had one rule only. If we held it and it rattled, crinkled, snap, crackled or,popped it was fair game for his stomach and warranted longing looks, woeful expressions and licking of chops until we acquiesced. Canine rules.

    Liked by 1 person

  10. This was hilarious, Dan. Dog math is very different … and yet, strangely logical. If I was a dog, I would approve of each of these requirements. I’m particularly fond of ‘Last bites multiply when items are divided’. Clever!

    Liked by 1 person

  11. Hi Dan – well Maddie’s got her maths right … adapts it to her needs – look she’s sleeping right now from overdose last bites … while Smokey’s obviously hard done by – she’s still feeding … but great post – fun to read … take care – get some of those bites in! Hilary

    Liked by 1 person

  12. According to Chickie, any time the can opener is used, the cat expects tuna or salmon. If there is no tuna or salmon, a bite of whatever is opened must be offered to the cat for inspection, even though it’s certain she’ll reject it.

    The full moon picture exceeds all expectations.

    Liked by 1 person

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