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10,000 random people from around the world have been invited to Mr. Foo's birthday party, and they are all very excited for it. However, he has devised a security system so only the smartest people can go to the party.

But there is a problem: there was a bug in the security system, and all the letters and digits have been replaced by "null" values. However, it is still possible.

Alex is heading to the door, and Mr. Foo tells him:

[none] [nothing] [null]
[none] [none] [nothing]
[null] [none] [nothing]

Alex answers,

[null] [null] [null] [none]

and enters the door to meet all his friends.

Beth gets told:

[nothing] [null] [nothing]
[nothing] [none] [nothing]
[null] [none] [nothing]
[none] [none] [nothing]
[nothing] [null] [nothing]
[nothing] [nothing] [none]

and says,

[null] [nothing] [null] [nothing]

and gets sent in, hoping for some nice biscuits and burgers.

Mr. Foo said to Carl,

[nothing] [null] [none]
[null] [none] [nothing]
[nothing] [none] [none]
[null] [none] [nothing]
[none] [none] [nothing]

Carl says,

[null] [null] [nothing] [none]

and went in, hoping for a few BFF's dance with him.

Then, Mr. Foo tells Dennis,

[nothing] [null] [nothing]
[nothing] [none] [nothing]
[none] [nothing] [null]

then Dennis says, "Um, um, uh, um...

[null] [nothing] [none] [none]

?"

Mr. Foo replied, "That ain't it, fool, cause [null] lost the war and [nothing] ain't neutral," and sent Dennis home.

Then Ellen was told,

[null] [nothing] [null]
[none] [null] [null]
[null] [nothing] [null]
[nothing] [null] [nothing]
[nothing] [nothing] [none]

. What should she say to get into the party?

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5
  • $\begingroup$ Are the names important? $\endgroup$ Mar 3 at 14:15
  • $\begingroup$ @1357924680a No. $\endgroup$ Mar 3 at 14:28
  • $\begingroup$ Shouldn't Beth have answered [null] [nothing] [null] [nothing] or does she get a pass on account of her good looks? ;) $\endgroup$
    – M Oehm
    Mar 4 at 18:55
  • $\begingroup$ Is the use of the three placeholders consistent? $\endgroup$ Mar 4 at 19:39
  • $\begingroup$ @WeatherVane Yes. $\endgroup$ Mar 4 at 19:56

1 Answer 1

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Ellen should say:

[none] [nothing] [none] [nothing]

Some observations:

There are three different values: [null], [none] and [nothing]. The guard's "question"s consist of several (three to six) chunks of three values. The guests' responses are always four values.

The code:

Three possible values that come in groups of three suggest a ternary representation of numbers. If that is true, the three values must represent the digits 0, 1 or 2 in some order. The groups of three "digits" can represent numbers from 0 to 26, which is handy for the 26 letters of the English alphabet plus a space/punctuation characer. The groups of four digits can represent numbers from 0 to 80.

(There's probably a hint in the guard's remarks to Dennis's answer, but if so, I don't get it. I just tried the 6 possible arrangements of digits.)

Anyway, ...

... it turns out that [null] is 0, [none] is 1 and [nothing] is 2. After replacing these digits and converting to decimal and, for the three-digit numbers, to a letter (1 = A, 2 = B, ..., 26 = Z), we get:

Alex: 120 112 012 ⟶ 15 14 5 ⟶ ONE.
    0001 ⟶ 1.

Beth: 202 212 012 112 202 221 → 20, 23, 5, 14, 20, 25 → TWENTY.
    0202 ⟶ 20.

Carl: 201 012 211 012 112 ⟶ 19, 5, 22, 5, 14 ⟶ SEVEN.
    0021 ⟶ 7.

Dennis: 202 212 120 ⟶ 20, 23, 15 ⟶ TWO
    0211 ⟶ 22 (wrong, should be 0002)

Ellen: 020 100 020 202 221 ⟶ 6, 9, 6, 20, 25 ⟶ FIFTY

It is clear that the guest should answer with the given number in ternary and with the appropriate "digits". Fifty is 1212 in ternary, so Ellen should say [none] [nothing] [none] [nothing].

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