Math & Logic Puzzles - Number Theory & Reasoning

Each day the frog nets 1 meter (3 up, 2 down). After 27 days, he is at 27 meters. On the 28th day, he leaps 3 meters, reaches 30 meters, and exits before slipping.

Your upstream speed is 7-3=4 mph. The bobber drifts at 3 mph downstream. Relative closing speed is 4+3=7 mph. For 14 miles, time = 14/7 = 2 hours. This classic puzzle works because the bobber's drift speed cancels out the stream's effect on your round trip.

With only 2 colors (black and white), taking 3 socks guarantees a matching pair by the pigeonhole principle. In the worst case, you pick one black and one white sock - the third sock must match one of them. You need only 3, not 6 or more.

The question states 'Mary's mum' - Mary is one of her children, so Mary herself is the fourth child. April, May, and June are the first three. This is a classic riddle that tricks you into thinking the answer should be another month name.

The friends meet in 3 hours since they close the 36-mile gap at 12 MPH combined (6+6). The pigeon flies continuously at 18 MPH for the full 3 hours, traveling 54 miles. The back-and-forth motion is irrelevant - only total flight time and speed matter.

In the classic pirate game theory, the senior pirate offers 1 coin to the 3rd and 5th pirates to secure their votes (since they would get 0 otherwise), keeping 98 for himself.

By elimination: Cal and Deb have pets with hair (mammals). Bob's pet can't fly. If the pets are Bird, Fish, Dog, Cat: Amy must have the Bird as it is the only one left that fits the logic of the others having mammals/non-flyers.

Since boys don't like soccer, Danny can only prefer Tennis. Audrey doesn't like football or soccer, so she prefers Kickball. Danny explicitly moved away from his football/kickball preference, confirming Tennis. By elimination: Jane-Football, Robert-Soccer.

The least common multiple (LCM) of 2, 4, 6, 8, and 10 is 120. This is the smallest integer divisible by all those numbers.

The smallest two-digit prime is 11. The greatest two-digit square is 81 (9^2). Their sum is 11 + 81 = 92.

The number 484 is a palindrome, its first digit is 4, and 4+8+4=16. It is also a square number (22^2). It follows 121 as a three-digit palindromic square.

For 22, both digits are 2, so the sum (2+2=4) equals the product (2×2=4). Also, 22 is a multiple of 11 (22 = 11 × 2). Options 20 and 24 are not multiples of 11, and for 23, the sum is 5 but the product is 6.

The first two numbers are 4 (average of 3 and 5) and 6 (average of 5 and 7). The next pair of twin primes is 11 and 13, whose average is 12. Option 9 is not the average of any twin prime pair.

The sum of two different cubes 1^3 (1) and 2^3 (8) is 9. 9 is a square number (3^2). This is the smallest square that is a sum of two distinct cubes.

Since a > b, a! = a * (a-1) * ... * (b+1) * b!. Therefore, a! is a multiple of b!, and the remainder of any multiple divided by its factor is always 0.

Numbers that are neither prime nor even are odd composite numbers. The first is 1 (by definition here), the next odd numbers are 3 (prime), 5 (prime), 7 (prime), and 9 (composite). Thus, 9 is the second.

The Fibonacci sequence continues: 21, 34, 55, 89, 144... Of these, 21, 34, 55 are not prime. The number 89 is prime and is the next prime Fibonacci number after 13. 79 is not a Fibonacci number.

The number 11 satisfies all conditions: 11/2 leaves remainder 1, 11/3 leaves remainder 2, and 11/4 leaves remainder 3. It is the smallest such positive integer.

The squirrel is the odd one out because it is the only land animal that cannot fly or appear in the sky. The eagle is a flying bird, the cloud is a sky phenomenon, and the plane is a flying machine - all three are associated with being airborne or appearing in the sky. The squirrel is fundamentally a ground-dwelling creature.

The pattern is based on the number of syllables or phonetic structure. Costa Rica (4) and Thailand (2) don't match simply, but Ivory Coast (3) and Ireland (2) are often paired in word puzzles based on starting vowels or syllable counts.