Math & Logic Puzzles

The pattern is adding 1 to each letter: CUT→BDTVSU (C→B, U→T, T→S), so TIP→SUHJOQ (T→S, I→H, P→O). This is a simple substitution cipher shifting each letter back by one in the alphabet.

The pattern is letter reversal: WOLF reversed is FLOW, so WARD reversed is DRAW. This tests the ability to recognize anagram-like relationships between words.

Using weights of 1, 3, 9, 27, and 81 kg allows measuring any integer weight from 1 to 121 kg by placing weights on either side of the balance. This works because these are powers of 3, and 1+3+9+27+81=121, covering the full range through balanced ternary representation.

Given x ^ y = 2x + y, we have 2 ^ a = a ^ 3. This means 2(2)+a = 2a+3, which simplifies to 4+a = 2a+3, giving a=1. Verifying: 2^1 = 2(2)+1 = 5 and 1^3 = 2(1)+3 = 5, both equal.

The sequence follows the pattern n³ - n². For n=1:1-1=0, n=2:8-4=4, n=3:27-9=18, n=4:64-16=48, n=5:125-25=100, so n=6:216-36=180. Alternatively, second differences are constant (6).

The colors listed are Blue, Red, Green, Orange, Violet, Yellow, Pink, Indigo. All except Pink are standard rainbow colors (VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, Red). Pink is the odd one as it's not part of the traditional rainbow spectrum.

Shanghai is the only non-capital city among the options. Paris (France), Washington D.C. (USA), and Vienna (Austria) are all national capitals, while Shanghai is a major city in China but not its capital (which is Beijing).

The number of handshakes among $n$ people is calculated using the combination formula $n(n-1)/2$. For 20 people, this is $20 imes 19 / 2$, which equals $10 imes 19 = 190$. Each person shakes hands with 19 others, but we divide by 2 to avoid double-counting.

1900 was NOT a leap year because it's divisible by 100 but not by 400 (century years must be divisible by 400 to be leap years). 1904, 1908, and 1912 were all leap years because they're divisible by 4.

The set of whole numbers includes 0 (0, 1, 2, 3...). Any product that includes zero as a factor results in zero. Therefore, the product of all whole numbers is 0, regardless of how many positive integers follow.

In 1983, the Prime Minister of India was Indira Gandhi. As a woman, she did not use shaving blades for facial hair, making 'None' the logically correct answer to this trick question.

The sequence is n^n: 1^1=1, 2^2=4, 3^3=27 (but the list says 9), 4^4=256, 5^5=3125. 9 is the odd one out because it is 3^2, whereas the pattern requires 3^3=27. Thus, 9 does not fit the n^n rule.

The pattern is (n * 2) + 1, then (n * 2) + 2, then (n * 2) + 3, etc. 42+1=9; 92+2=20; 202+3=43; 432+4=90. The next step is 90*2+5 = 185. 170 and 222 do not follow this incremental multiplier-addition rule.