This is similar to the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles. Giving credit where credit is due.

I was sitting at Landra Hort's Mystery Ice Cream Shoppe slurping on the last of my Birou Sundae when I noticed a man walk up to the counter and ask the cashier for a free scoop. The cashier said, "Give me a word with no two." The man said to her:


The cashier smiled and said, "Excellent! What flavor would you like?"

The man asked for the smooth Mean Chart Hug Nag, and received one scoop for free.

Mystified, I watched as someone else walked in and asked for a free scoop. The cashier asked the same question: "Give me a word with no two." The customer said:


and received his scoop of the spicy Devious ice cream. Determined to find the pattern, I sat and watched day after day, making a note of what words had "no two." Here is a small sample:

laptop, mathematics, mist, overflow, green, three, four, score, cream.

And a few words that didn't make it:

puzzling, stack, exchange, (someone had ideas, I guess ;D) red, one, two, upvote.

One poor fellow was denied after giving the word


He clarified that he meant flour rather than flower and received his scoop of Grape Nut Leper Lin.

For what it's worth, some of the other flavors that I heard ordered were Mix-o Hone and H. M. Moe.

Confident of my success, I went up to the counter after a week of observation and asked for a free scoop of ice cream. The cashier, as usual, said, "Give me a word with no two." I responded with


and happily enjoyed my free scoop of Ring Herder ice cream.

What other words could get you some ice cream?

  • $\begingroup$ I used a computer to check which do and do not have a two in them, so hopefully this one won't have any mistakes in it @Deusovi $\endgroup$
    – Brandon_J
    May 31 '19 at 17:18
  • 4
    $\begingroup$ He should have given you a scoop of BnJ "Radon" ice cream instead. $\endgroup$
    – Gareth McCaughan
    May 31 '19 at 18:17
  • $\begingroup$ @GarethMcCaughan He could have, but that would have been cruel to would-be solvers. At any rate, I prefer the Jon Brand (although Radon is a very close second). By the way, should you ever visit Landra's place, the "ug" in Mean Chart H ug Nag is not pronounced. $\endgroup$
    – Brandon_J
    May 31 '19 at 18:22
  • 3
    $\begingroup$ Other words: I will give you 20 dollars :) $\endgroup$
    – Duck
    May 31 '19 at 22:28
  • 1
    $\begingroup$ @Brandon_J awful, that’s actually awful of you. (+1) $\endgroup$
    – El-Guest
    Jun 1 '19 at 16:24

Here's some other words that should get you free ice cream:


But why? The answer lies within

Summing the letters in the word (where A=1,Z=26) and then converting the sum to binary.
If the number has a 1 in the second digit place, then that means it has a two.

Words with no two:

ice:   9  +  3 + 5          = 17 = 010001
the:   20 +  8 + 5          = 33 = 100001
cream: 3  + 18 + 5 + 1 + 13 = 40 = 101000

Words with a two:

two:   20 + 23 + 15         = 58 = 111010
red:   18 +  5 + 4          = 27 = 011011
stack: 19 + 20 + 1 + 3 + 11 = 54 = 110110

Now the only question I have is what kind of training the cashiers go through to figure these out.

  • $\begingroup$ This is correct! Checkmark will come soon. $\endgroup$
    – Brandon_J
    Jun 1 '19 at 21:13

I’m thinking this is wrong, because there are some words that break the pattern, but could it be that

When you translate each word using A1Z26 and then add all of the numbers together, a word that gets you ice cream is even (as in flour) and a word that doesn’t is odd (as in flower)?

So a word that could get you ice cream is


I have no idea if this has anything to do with anything, but

All of the ice cream flavours are anagrams of prominent PSE users:
Landra Hort: Rand al’ Thor
Birou: Rubio
Mean Chart Hug Nag: Gareth McCaughan
Devious: Deusovi
Grape Nut Leper Lin: GentlePurpleRain
Mix-o Hone: Hexomino
H. M. Moe: M Oehm
Ring Herder: Red Herring

So could I have a scoop of

Lug’s Tee ice cream??

  • $\begingroup$ Looks to me like this gives the wrong result for "lemonade", "mist", "green", "stack", "one", "two", and "ice". $\endgroup$
    – Gareth McCaughan
    Jun 1 '19 at 15:16
  • $\begingroup$ Your answer is similar in style to the final answer, so props! Incidentally, "guest" is a word with no two (as is "el"), but it appears that you got that ice cream by luck. $\endgroup$
    – Brandon_J
    Jun 1 '19 at 15:17
  • $\begingroup$ Also, the condition seems almost backwards relative to the name it's been given. $\endgroup$
    – Gareth McCaughan
    Jun 1 '19 at 15:17
  • $\begingroup$ @GarethMcCaughan correct; this rule is not the answer. $\endgroup$
    – Brandon_J
    Jun 1 '19 at 15:18
  • $\begingroup$ @Brandon_J "A1Z26" is the usual term, I think. $\endgroup$
    – Gareth McCaughan
    Jun 1 '19 at 15:20

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