# Analogy with Number

The given analogy is

343 : 989 :: x : 669

What is x?

1. 223
2. 332
3. 333
4. 233
• What are the : and :: denoting? Are they operators? Relations? – Galen Apr 19 '20 at 18:52
• If they're operators, what are their definitions? If they're relations, what are their definitions? – Galen Apr 19 '20 at 19:02

Option #4 $$-$$ $$233$$

Reason:

To get from the number on the left to the number on the right, triple the first number, double the second, and triple the third.

$$343 : 989$$

$$3\times 3 = 9,\ 4\times 2 = 8,\ 3\times 3 = 9$$

$$233 : 669$$

$$2\times 3 = 6,\ 3\times 2 = 6,\ 3\times 3 = 9$$

option 1. The left side is a cipher of the right side: 3 ↦ 9, 4 ↦ 8, and given the options, we must have 2 ↦ 6. So the "encoded" version of 669 is 223.

C : 333. From right to left, half even numbers and divide odd multiples of $$3$$ by $$3$$.

• You could also put that as rot13(qvivqr rnpu ahzore ol gur svefg cevzr ahzore vg vf n zhygvcyr bs). – Egor Hans Mar 31 '20 at 8:27
• Or in other words: ercynpr rnpu ahzore jvgu vgf ynetrfg snpgbe (bgure guna vgfrys) – Matt Mar 31 '20 at 12:25

the first choice, 223. Each digit of the first term in each pair is $$1$$ less than the length of the English name of the corresponding digit in the second term in that same pair.

I know this is answered and ticked, but:

1. 223

Add 4 to even digits and 6 to odd digits.

This type of puzzle is an exercise in mind reading. All 4 answers have roughly equally valid logic supporting them, so you have to "read the mind" of the person posing the question to get the "correct" answer.

Other answers have explained why 3 of the 4 choices are logical solutions. The remaining puzzle is therefore to find a similarly convincing explanation for the remaining choice. Here is mine:

#2: 332

because

If we rank the digits, the second number of each pair is the opposite of the first. For example, 343 has the pattern low-high-low, and the opposite of that is high-low-high, which 989 fits. In the second pair, we see 669, which is low-low-high, so we need to find a number with the opposite pattern, high-high-low. Only choice #2 fits this.