# The ice cream puzzle

I am a new user, and I made this puzzle myself, but I lost the answer key, can anyone solve it so I can make a new one?

The owner of the ' Super Ice Cream' shop was terrified. One of his workers was caught putting a poison in one of 10 possible flavours: Strawberry, Chocolate, Vanilla, Green Tea, Cookies & Cream, Coffee, Taro, Bubble Gum, Tutti Frutti, and the day's special: Rainbow Unicorn. The owner filled 10 injections with a special truth telling potion to question ten witnesses. But there's a catch:

The worker who had put the poison was too scared, so he replaced some of the injections with a lying potion and mixed one with both potions so that that person's answer is totally random. Each person's answer could vary from 1-2 answers. A truth-teller's 2 answers are both the truth. A liar's 2 answers must make both are lies. The person who's answer is random can have these possibilities if he gave 2 answers: one is a lie, both are lies, or both are the truth.

• A states out that he saw the worker put the poison in the chocolate flavour.
• B says that C is a liar.
• C calls out that either taro or coffee have the poison.
• D says that the strawberry is poisonous and that F is truthful.
• E states out that the poison is in either the tutti frutti or the green tea.
• F calls out that the bubble gum is poisonous.
• G's statement is that the poison is NOT in the rainbow unicorn.
• H's statement is that C is truthful.
• I utters that vanilla has the poison and that J is a liar.
• J utters that E is a liar.

The owner knew that A is a liar, J is a truth teller, D is the person who answers randomly, and that there are more liars than truth tellers. The question is: Which flavour is the poison in?

P.S. I don't know if there are more than 1 solutions, so if there are, how many in total?

• I made the puzzle text only to maybe throw you all off, so sorry ;)
– user71418
Sep 16, 2020 at 4:33
• So, everyone but the owner knows where the poison is, and everyone but the owner knows which injection everyone got?
– Bass
Sep 16, 2020 at 6:11
• Yes, but it is highly unknown to the owner
– user71418
Sep 16, 2020 at 10:35

I found six possible solutions

There are a couple things we can determine straight away

Because we're given that A is a liar, we know the chocolate is not poisoned. Because we're given that J is a truth teller, I (who claimed J lied) and E are liars, so the vanilla, green tea, and tutti frutti are all safe. Finally, because B and H made opposite claims, one is a liar and the other is telling the truth. So we know of three liars, one truth teller, and the random. Thanks to the condition that there are more liars than truth tellers, we know at least two of BCFGH must be liars.

Regarding D

D's statements are worthless - because D is random the truthfulness of the two statements are independent of each other. So even after we decide whether or not F told the truth, that doesn't tell us anything about whether or not the strawberry is poisoned.

From there

Any of the remaining flavors could possibly be poisoned. If one of the taro or coffee is poisoned, C and H told the truth, B lied, F lied, and G told the truth, so we've satisfied the condition of at least two more liars. If one of the strawberry, cookies & cream, bubble gum, or rainbow unicorn is poisoned, C and H lied, and B told the truth. We already have the two liars we need, so it's okay if F tells the truth (when it is the bubble gum that's poisoned), or for G to lie (rainbow unicorn is poisoned).

General comment on the puzzle itself:

It's an interesting idea for a puzzle, but you don't have enough constraints for it to have a unique solution. Needing to have more liars than truth tellers could have made for an interesting way to solve it, but as you can see it was trivial to get enough liars in each case. You didn't actually need to say that J is a truth teller - I's statement ties to J, and J's statement ties to E, and the statements by I and E can't both be true. Getting something like that in there for a few of B, C, F, G, and H could have narrowed down the possibilities.

• I remember the solution being cookies and cream, but if that is so, who are the liars and truth-tellers? I cannot tell
– user71418
Sep 16, 2020 at 10:36
• And, I made this puzzle way before the pandemic, so I wasn't an expert back then
– user71418
Sep 16, 2020 at 10:38
• In order for it to be cookies & cream, then rot13(O, T, naq U ner gehgushy, rirelbar ryfr vf n yvne, naq vg vf vzcbffvoyr gb gryy jurgure be abg gur cbvfba vf va fgenjoreel be pbbxvrf & pernz orpnhfr Q nafjref enaqbzyl) Sep 16, 2020 at 11:28
• I'll accept this answer, thanks
– user71418
Sep 16, 2020 at 13:45

I find only one answer: Rainbow unicorn is poisonous.

Considering the "lateral thinking", and the explicit statement of new user that he is a new user, there is one 'hidden truth teller': the poster. So there should be two liars more in the actual puzzle. Solving it with that, I come to the above conclusion.

• I'm sorry with the confusion with the lateral thinking tag, so I deleted it
– user71418
Sep 16, 2020 at 12:39
• Even if there were a "hidden truth teller", there's still possibilities where the strawberry or cookies and cream could have been poisoned. Jul 19, 2021 at 19:18