Glenn's "Half-a-Time" Explanation (The stuff on this webpage was mentioned on page 163 in my book.)

Illustration of a boy (Glenn) smilingHello. My name is Glenn Philips.

Ronald Mack, my friend and classmate, asked me to explain why some whole numbers cannot be split into parts even though we sometimes speak of them that way.

First let me say I very much enjoyed reading the book Ronald wrote.

In that book, Ronald described the monthly poker game attended by his father and Georgie Sinkoff’s father. He wrote:

I think there are eight men who play, but they do it at a different house each time, so they’re only at my house one and a half times each year. (Okay. I know that it’s impossible to be at my house a half of a time. But twelve months divided by eight men does equal 1.5, so…Aha! I just called Glenn Philips. He said I am right, but there’s a better way to say it: They’re only at my house three times every two years.

Yes, it is impossible to be somewhere a half of a time. Yes, there is! But it's too gross for fifth graders.That’s because some things—like trips to the post office, or home runs, or Vice Presidents of the United States—cannot be split. There is no such thing as “half of a home run” or “half of a Vice President”

Here’s a way to look at the poker game question. Assume that the eight men who play are Messrs. A, B, C, D, E, F, G, and H. They agree to host the game each month at a different man’s home. playing card suits: spade, heart, diamond, clubMr. A hosts in January…Mr. B in February…Mr. C in March…and so on. Look at the table below. After one year, half of the men (Messrs. A, B, C, and D) would have had two games at their homes, but the other half (Messrs. E, F, G, and H) would each have hosted only once. On average, each man would have hosted 1.5 games per year.

Two tables, titled "Year One" and "Year Two". Both tables have two columns, the left column being the months from Jan to Dec, and the right column being letters.
Year One
Jan - A
Feb - B
Mar - C
Apr - D
May - E
Jun - F
Jul - G
Aug - H
Sep - A
Oct - B
Nov - C
Dec - D

Year Two
Jan - E
Feb - F
Mar - G
Apr - H
May - A
Jun - B
Jul - C
Aug - D
Sep - E
Oct - F
Nov - G
Dec - H
But as I told Ronald, it might be clearer if he said, “Each man hosted three games every two years.” That also averages 1.5 times a year.

I hope this explanation is clear. If you have further questions, please ask them below, and I (Glenn Philips) will answer.

(Cheesie writing now: Glenn is really smart. You can ask him super hard questions!)

Book 1

Mystery, mice, and money at the end of fifth grade!

from my book

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Comments from my Readers & Friends

  1. Yeah the half a Vice President is if someone took a sword ⚔️ 🗡 and cut them in half!!!!!!!!!!!!!!!

    1. As Cheesie says in his books, everything he writes is true. And since Cheesie writes realistic fiction, everything he writes about me is both realistic and fictional, but also true. For personal privacy reasons (Gloucester is an actual town in Massachusetts), my mother has advised me to be no more specific than that. I hope that helps.

    1. Perhaps you will think I am bragging, but this was not a very difficult problem. It took me only one minute.


    2. The other two solutions are incorrect because the R becomes a zero, which in normal mathematical practice is an invalid leading digit in the five-digit number signified by RARES.

  2. Glenn, solve this.


    Each letter is a variable, and different letters are different 1 digit scalars.

    PLEASE don’t look this up on Wikipedia.
    I am in 4th grade and it took me 15
    minutes. What does each letter stand for?

    1. 9567 + 1085 = 10652
      Thank you for this puzzle., Here’s how I did it.
      Obviously M=1 because S+M cannot be larger than 18.
      Then, since M=1, O must equal either 1 or zero and S must be 8 or 9.
      Then, since E+O{the letter O}=N, and N and E are different, N must be one or two larger than E.
      The rest was easy. perhaps I’ll let others figure out the remainder of the puzzle.

  3. or you could have just said that if it’s 1.5 a year, then in two years, you would just double it and a .5 + a .5 = 1 so then you add the other 1.’s
    (you have two of them) to equal 3. or you could have just said 1.5+1.5= 3, or 1.5(yearly)* 2(years)= 3. if that made any more sense.

  4. In school I am in the G.T.E.(Gifted and Talented Education) program! (Huge acomplashment and means I am smart).

    1. ME too! I’m in gifted math and language arts, which are the only things in my grade that you can be advanced in.

    1. I cannot tell how smart you are from this one comment, but it does appear that you know how to divide.

  5. im kind of a nerd myself so here goes. u cant play half a poker game! it would me for two years 1 and a half plus one and a half equals three!

    1. Nerds rule! (But I am also lots of other things beside a nerd: athlete, good student, creative, goofball, etc.)

  6. INCREDIBLE! Except your wrong about the largest star ever discovered. Actually its VY Canis Majoris. It is one billion more times then the sun. So that means one billion suns can fit in it. It is 4,892 light years away. Great job anyways.

    1. 299,792,458 meters per second; 186,282 miles per second; 299,792.458 kilometers per second. This is the sort of information you can easily look up on the internet.

  7. Also the average for each man to host a year would be 1.75 because 1.75 is in the middle of 1.5 and 2.00. So that means an average to at least host a year would be is 1.75. Also the average to host two years will be 3.00 since every man hostesd 3 times those two years and three years will be 4.00 and so on so for.

  8. Glenn i have a really hard question. It is what is the largest star ever discovered and what is the smallest country on earth.

    1. The largest star currently discovered is NML Cygni. It is a red hypergiant star and is about 1,650 times the Sun’s radius. This means if its center were where our sun’s is, its surface would be so far out, it would swallow up Mercury, Venus, Earth, Mars, every object in the asteroid belt, and Jupiter…with room to spare! It is about about 5,300 light-years away from Earth. It was discovered in 1965 by Neugebauer, Martz and Leighton. That’s why it’s named NML.

      The smallest country is Vatican City (0.2 sq. miles). It is completely surrounded by Rome, Italy.

    1. That is very nice of you to say. Cheesie actually asked me if I would like to write a chapter in one of his upcoming books. I am considering it. Perhaps I will.

  9. Glenn – You made it so hard! Why didn’t you just do 24 months divided by 8 men?

    1. I actually did say that. I wrote above: “But as I told Ronald, it might be clearer if he said, ‘Each man hosted three games every two years.'”

      But people usually refer to events in terms of what occurs in one year, not in two years. That’s why I explained it that way.

      (And I would like to mention that Cheesie said he met Mrs. Webb. “She is very nice,” he told me.)

    1. The title of my books says I am not a genius, so how should I know what that Japanese means? Gimme a break!

    2. Only reason is you said it was katakana, and I asked my dad…he said that’s some kind of Japanese writing. But I don’t know what it means.

  10. Solve Einstein’s Riddle. The reason 98% of the world cannot figure it out is because they over look it. (I know the answer ;D.)
    Here it is
    There are 5 houses in 5 different colors. In each house lives a person with a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage.
    The question is: Who owns the fish?


    The Brit lives in the red house.
    The Swede keeps dogs as pets.
    The Dane drinks tea.
    The green house is on the left of the white house.
    The green homeowner drinks coffee.
    The person who smokes Pall Mall rears birds.
    The owner of the yellow house smokes Dunhill.
    The man living in the center house drinks milk.
    The Norwegian lives in the first house.
    The man who smokes Blend lives next to the one who keeps cats.
    The man who keeps the horse lives next to the man who smokes Dunhill.
    The owner who smokes Bluemaster drinks beer.
    The German smokes prince.
    The Norwegian lives next to the blue house.
    The man who smokes Blend has a neighbor who drinks water.

    1. If you’re not a genius, how come you know lots of words and you are way better in math than I am? You ARE a genius. You’re a genius because you wrote your own book! Face it man. YOU’RE A GENIUS!!!!

    2. Glenn Philips is way smarter than I am. He’s a genius…not me. (But thanks for the compliment.)

    3. Hi there, Jordan. I’m sorry but that’s all I’m supposed to give you. (i sounded like a nerd!!!! XD LOL ROFL)

    4. i did it!!!!!!!! i guessed so i would get the other answers and i guessed right!!!!!!! im in 4th grade!!!!!!!!!!!!!!

    1. I could use a calculator to figure it out easily. But I know a trick that gives an excellent estimate. Since 25 x 25 = 625, then 2500 x 2500 = 6,250,000, so I would guess a little higher…maybe 2,504 would be a good guess.

      I think Stephanie (above) used a calculator!

  11. WOW!!how did you or glenn know that?!?did you use your noggein?? pleese reply and tell me.

    1. This actually isn’t very difficult. Just look at the tables above. I believe my explanation is clear.

    1. But then it’s not really any part of a home run. It’s just a double. Which is quite good. I’d very much enjoy hitting doubles.

    2. Yes, I see what you’re talking about. A run would score, but it still isn’t half of a homer.

    3. it could be, because a hom run is a score on one hit when you round FOUR bases. So since you reach second which is half of what you reach in a homer, but a run still scores, then it could be half a home run.

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