Impossible Brain Breakers Trivia Quiz

Answer: Back

Start out by factoring the product.
In this case, you'll find 66 equals 2*3*11. However, you need FOUR letters, so at least one of those letters will be the A.
By transforming the other factors into letters, you should find B, C and K.
Now you an scramble those letters and you'll find BACK.
If you were to multiply the different factors and use more than one A, you could come up with one of the following letter sets: AAFK or AACV, which don't scramble into body parts.

Answer: Ear

Factoring 90 gives the following result: 90 = 2*3*3*5.
You only need three letters, so you should combine at least two of the factors.
Now you can start a process of trial and error. Let's see what happens if you use the "2" for a B. The other letters are IE or CO, so you end up with either BIE or BCO, which can't be scrambled into body parts.
If you use the "2" and one of the "3"s together, you come up with FOA or FCE. These are not the right combinations either: try scrambling these letter combinations.
By using the "2" and the "5", you would reach J. The other letters are AI or CC. No positive result here neither: JCC cannot be scrambled into any English word, and JAI is no anagram of any body part.
So the "2" and both the "3"s have to be multiplied. You then obtain R (2*3*3=18), E and A (remember the solution has three letters, so you need an A). REA can be scrambled into EAR.

Answer: Head

Factoring 160 gives 2*2*2*2*2*5.
As the difficulty increases by having more factors, you could try eliminating all letters that can't be formed by the factors and searching for the vowels first.
Which letters can be made with the aforesaid factors? A, B, D, E, H, J, P and T.
So the vowels in this four letter word should be A and/or E.
You'll also notice that you can use only one of the letters E, J and T, for all these can account for the single "5".
Now you can start trying out some solutions.
Let's take TA and you come up with either TAHA or TABD. This is not the right solution.
Starting the equation by JA, you're left with one of the following: DD, BH or PA. Combining these would give JADD, JABH or JAPA - quite droll letter combinations, but sadly no anagrams of body parts.
So you end up with E and five instances of the "2". Here are several possibilities: EPBA, EHBB, EHDA, EDDB. Analysing these options will give you the correct solution: HEAD.

Answer: Arm

Factorization of 234 renders 2*3*3*13.
Let's see if the "13" can be combined with the "2" to make a Z, or if the "13" has to be used as M.
Z can be combined with AI or CC. Neither of these combinations gives us an anagram of a body part.
So we should use an M. This leaves us with one of the following combinations: AR, BI, CF. MCF nor MBI give the desired result, so we'll fill in ARM.

Answer: Leg

Start factoring and you'll find 420=2*2*3*5*7.
The "7" can stand for G, N (=7*2) or U (=7*3).
If we choose a U, we can combine the following: UAT, UBJ or UDE. This doesn't give the correct answer.
Should we try out the N? Let's see: we get NBO, NCJ, NFE. Neither of these letter combinations give what we're looking for.
So we go for the G. What's left? DO, FJ or LE. Now we'll fill in LEG.

Answer: Hand

Let's begin by factoring. You'll find 448 = 2*2*2*2*2*2*7.
You'll need 4 letters, of which at least one vowel (there are no body parts of four letters without any vowels). Only one vowel qualifies: the A. There is no E (fifth letter), I (ninth letter), O (fifteenth letter), U (twenty-first letter, so the product of a word containing a U has to be a multiple of 3) or Y (the twenty-fifth letter).
Now you can use the "7" as a G or as a N (14=7*2). If you try out the G, you get GADP or GAHH, which are no correct solutions.
So you'll have to use NA. The remaining letters should form BP or DH, and the last option gives us the right answer: HAND.

Answer: Eye

Factoring 625 shows us a limited set of possibilities. Indeed: 625 =5*5*5*5.
Taking into account you have only three letters to use, there are only two possible letter combinations: either YYA or YEE.
Evidently you can anagram the latter option into an EYE.

Answer: Toe

Factoring 1,500 gives us 2*2*3*5*5*5.
This means we can use following letters: A, B, C, D, E, F, J, L, O, T, Y. There is no easy solution here, we'll have to try out everything.
Let's start with an A: two remaining letters won't suffice, for there are only 26 letters in the alfabet, and 26*26 is only 676.
The same goes for B as well: the remaining product is too big.
If we try C, we end up with T and Y. You can scramble CYT, but not into a body part.
D would leave us with O and Y. DOY is no anagram of a body part, either.
E is good, as I'll show you later on.
F won't do: you end up with JY, and FJY doesn't help us.
J can give FY (already discussed before) or OJ. JOJ is not correct.
L would leave us with E and Y. LEY is interesting, but not quite what we're looking for.
I'll come back on O and T in a minute.
Y can lead to several of the aforesaid wrong combinations: CYT, DOY, FJY or LEY.
Now you see I've skipped E, O and T. These letters form an easy anagram: TOE.

Answer: Lip

This one is very tricky, for the product is decomposed in a large number of factors. So there are plenty of combinations to rule out.
1,728 = 2*2*2*2*2*2*3*3*3.
Possible letters are A, B, C, D, F, H, I, L, P and R. This isn't very useful to set us on the right track.
But choosing the correct vowel will do. If you take A, you're left with a too large number to decompose into only two letters. So you'll need an I.
What's left after we take an I (3*3)? Well, the rest is either HX or PL.
Now, scramble the two options: IHX doesn't make any sense, IPL gives after scrambling LIP.

Answer: Skin

Factoring leads us to the following equation: 26,334 = 2*3*3*7*11*19.
Now "19" corresponds to S, so the correct answer will contain an S.
"11" can be used for K or V (2*11). Let's start with the V. Adding the other letters, you'll end up with either SVCU or SVIG, which are no anagrams of body parts.
Thus you'll need SK. The remaining letters can be FU, RG or NI. You can immediately eliminate SKRG, for it contains no vowels.
Scrambling around SKFU doesn't add up to the right solution, SKNI does: it is the SKIN.