Cartalk Puzzler: An Interesting Series of Numbers

A new cartalk puzzler is up.

When my kids were in school, they, like all the other kids I guess, had to learn their numbers. So each day for homework, they would bring home a list of numbers on a piece of paper, and they were asked to write out the letters that spelled that number, right next to each of them. So the number seven would be there, there’d be a blank space, the kids would have to write S – E – V – E – N. And of course they were also asked which numbers were spelled out by the various combinations of letters, so they’d see S – I – X – T – Y and write Sixty, etc.

One day, son number two presented me with a list of numbers and he said, “These numbers are different. There’s something special about them.” Here are the numbers:

Four, Six, Twelve, Thirty, Thirty Three, Thirty Six, Forty, Forty Five, Fifty, Fifty Four, Fifty Six, Sixty, Seventy, Eighty One, Eighty Eight, Ninety, and a Hundred.

Now there are no other numbers between one and a hundred inclusive that share this same characteristic. There’s something unusual about these numbers that son number two figured out. And I’ll give you an additional hint that order does not matter. The best hint is that he determined that these numbers should be on the list perhaps from his homework assignment.

What is special about this list of numbers?


Update (9/25/11): Answer is up.

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12 Responses to Cartalk Puzzler: An Interesting Series of Numbers

  1. Andrew says:

    Until “a hundred” I was leaning towards the number of letters in the written form being a factor of the named number. I can’t claim to have exhaustively checked all the other numbers in the 1-100 range, but the distribution of number-name lengths seems to point towards no.

    Am I missing something obvious on “a hundred”?


  2. Dan says:

    The number divided by the amount of letters is always even?
    That’s what I’ve got.

    • Thaddeus says:

      That does not work Dan. Eighty one is nine letters so the answer would be odd. 81 / 9 = 9. Nine of course is odd.

      Did I misinterpret what you said?

  3. Dan says:

    I actually meant the combination of the numbers, I must have left that out.
    So 81 would be 9, and 12 would… I just noticed that my pattern is inconsistent. I must be wrong. Whoops.

  4. Dan says:

    Oh, and by even I meant without any fractions, a whole number. I find that doesn’t work with twelve since it’s 3 divided by 6, and thats 0.5.

  5. Rich says:

    Andrew, You got it. As Dan pointed out, “one hundred” works. Also, Ray mentioned that his “son # 2” came up with the list but he didn’t say when. I think Andrew got it.

  6. Scott says:

    Not buying it. You can’t change the puzzle to fit the solution. If you have to do that then the puzzle is invalid.

  7. Ernest Manfred says:

    Dan is right. No other numbers between 1-100 have that property.

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