Math Puzzles & Logic Problems

Let x be games won by 'me' and y be games won by the cousin. x - y = 18 and y = 9. Therefore, x = 27. Total games = x + y = 27 + 9 = 36. Since they played one game per day, the cousin stayed for 36 days.

For the number 27, the sum of digits is 2 + 7 = 9. Multiplying the sum by 3 gives 9 * 3 = 27. This satisfies the condition. Other options like 36 (3+6=9, 93=27) or 30 (3+0=3, 33=9) do not match.

A fair die has numbers {1, 2, 3, 4, 5, 6}. The prime numbers are {2, 3, 5}. Among these, the odd prime numbers are {3, 5}. There are 2 favorable outcomes out of 6 total, so the probability is 2/6 = 1/3.

To ensure one of each, consider the worst-case scenario: you pick all 60 white balls and all 40 black balls first. At this point (100 balls), you still don't have a red ball. The 101st ball must be red. Thus, 101 balls ensure all colors.

The probability of the first card being a King is 4/52. Since it is without replacement, the probability of the second card being a King is 3/51. Total probability = (4/52) * (3/51) = (1/13) * (1/17) = 1/221.

Total outcomes for 4 tosses = 2^4 = 16. 'At least 3 heads' includes 3 heads (4C3 = 4 ways) and 4 heads (4C4 = 1 way). Total favorable outcomes = 4 + 1 = 5. Thus, the probability is 5/16.

For a 4-digit number using {9,8,7,5,0}, the first digit cannot be 0 (4 choices). The second digit can be any of the remaining 4 (including 0), the third digit 3, and the fourth digit 2. Total = 4 * 4 * 3 * 2 = 96.

This is a riddle that plays on expectations. The question says "Larry's father has five sons" and lists four sons with number names. The fifth son is Larry himself - it's his father, so Larry is one of the sons. The pattern of number names (Ten, Twenty, Thirty, Forty) is meant to mislead you into thinking the answer should be "Fifty."

The logic is the number of letters in the English word for each number: Nine(4), Twenty-one(9), Twenty-two(9), Twenty-four(10), Eight(5), Seven(5), Ninety-nine(10), One hundred(10). For 16 (Sixteen), there are 7 letters. For 17 (Seventeen), there are 9 letters. The stored answer 9 refers to Seventeen.

The numbers from 90 to 100 inclusive are 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 (total 11 numbers). Among these, only 97 is a prime number. Therefore, the probability is 1 out of 11. Other options assume a total of 10 numbers, which is incorrect for an inclusive range.

A parallelogram satisfies all three conditions: opposite sides are equal in length, opposite sides are parallel, and opposite angles are equal. A trapezium (US: trapezoid) only has one pair of parallel sides, a rhombus has all sides equal (which is more restrictive than the condition stated), and a kite has two pairs of adjacent equal sides, not opposite.

The surface area of a cube is calculated by the formula 6s^2, where s is the edge length. For a cube with edge 4 cm: 6 x (4 cm)^2 = 6 x 16 cm^2 = 96 cm^2. Option A (64 cm^2) would be the volume (4^3), option C (16 cm^2) is just s^2, and option D (48 cm^2) might result from incorrectly using 3s^2 instead of 6s^2.

Let the son's current age be x years. Then the father's age is x + 30 years. After 5 years: son's age = x + 5, father's age = x + 35. Given that father will be thrice as old as son: x + 35 = 3(x + 5). Solving: x + 35 = 3x + 15, so 2x = 20, x = 10. Father's present age = 10 + 30 = 40 years.

The family has: 1 mother + 1 father + 7 daughters + 1 brother (the same brother for all daughters) = 10 people total. The key insight is that 'each daughter has 1 brother' means there is one male child who is the brother to all 7 sisters.

With 10 people, each person shakes hands with 9 others. This gives 10 × 9 = 90 handshakes counted. But each handshake involves 2 people, so we've counted each handshake twice. Total handshakes = (10 × 9)/2 = 45. Formula: nC2 = n(n-1)/2 for n people.

Day 1: read 120 pages (240/2), 120 left. Day 2: read 60 pages (120/2), 60 left. Day 3: read 30 pages, 30 left. Each day you read half of what remains, so you always have half left. You'll approach completion but never actually reach it - it's an infinite series: 240 + 120 + 60 + 30 + ... = 480 pages total.

This is a pattern completion puzzle where the first statement '1=5' establishes the rule. If 1 equals 5, then by the same rule, 5 must equal 1. The pattern is: each number equals 5 raised to that power, but completing it requires returning to the initial pairing.

Count all occurrences of digit 7 from 1 to 100: In units place (7, 17, 27, 37, 47, 57, 67, 77, 87, 97) = 10 times. In tens place (70, 71, 72, 73, 74, 75, 76, 77, 78, 79) = 10 times. Total = 10 + 10 = 20. Note: 77 contains two 7s and is counted in both groups.

All 12 months of the year have 28 days. February has exactly 28 days (or 29 in leap years). The other 11 months all have 28 days as part of their 30 or 31 days. This is a classic trick question testing whether you focus on 'at least 28' versus 'exactly 28'.