Logic Puzzles and Math Fundamentals

The water-lily doubles in size each day. If it covers the entire pool on day 20, then on day 19 it must have covered exactly half the pool (because doubling half gives the full pool). This is a classic exponential growth problem - the key insight is that going backwards one day means halving the coverage. The distractors (10, 15, 18) come from mistakenly thinking halving the days gives half coverage, but exponential growth doesn't work that way.

16 × 16 = 256. This is basic multiplication - the square of 16.

The factorial of 5 (5!) is calculated as 5 * 4 * 3 * 2 * 1, which equals 120.

18³ = 18 × 18 × 18 = 5832. Calculate 18 × 18 = 324, then multiply by 18 again.

To convert 16 to binary, divide by 2 repeatedly: 16/2=8(R0), 8/2=4(R0), 4/2=2(R0), 2/2=1(R0), 1/2=0(R1). Reading remainders upwards gives 10000.

100 in decimal equals 64 in hexadecimal. Divide 100 by 16: 100 ÷ 16 = 6 remainder 4, so the hex representation is 64.

A cube has six identical square faces. If the side length is 'a', the area of one face is a*a. The total surface area is the sum of all six faces, which is 6 * a^2.

From the given relationships, we can establish that Natalie is shorter than both Kate and Sammy, while Sammy is shorter than both Kate and Carly. Since James is taller than Kate and Carly, and no one is mentioned as being shorter than Natalie, she must be the shortest person in the group.

Rachel/Jessica > John. John > Lara > Maria/Sally. Comparing John, Maria, Lara, and Sally, John is taller than Lara, and Lara is taller than Maria and Sally. Thus John is the tallest of that specific group.

Joy > Brian > Cassie > Val > Geoff. Since Geoff is shorter than Val, Val is not the shortest; Geoff is. Therefore, the statement 'Is Val the shortest?' is False.

Lorraine is taller than Robert and Jordan. Robert is taller than Jordan, Peter, and Kylie. Since Lorraine is taller than the tallest of the rest, Lorraine is the tallest.

Luke > Bianca > Cathy > Nathan. Since Bianca is taller than Nathan and Cathy, and Cathy is taller than Nathan, Nathan is the shortest.

Danny > Elise > Lisa. Since Danny is taller than Elise and Elise is taller than Lisa, Lisa is the shortest among the three.

We know Brett > Shannon > Rene. We also know Brett > Mel. However, there is no information comparing Mel to Shannon or Rene, so the shortest person cannot be determined.

The relationships establish that Fiona is taller than both Harry and Will, while Harry is taller than Will, Mike, and Sophie. Since no one is described as being taller than Fiona, she must be the tallest person. The height order is Fiona > Harry > Will > Mike, with Sophie somewhere below Harry.

Tamara > Ben, Ben > Matt, and Matt > Tom. Tamara is taller than Ben, who is taller than Matt and Tom. Thus, Tamara is the tallest.

Alan is taller than Jen and Sue. Jen is taller than Sue, and Sue is taller than Dick. Betty is shorter than Dick. Therefore, Alan is at the top of the height hierarchy.

The chain of relationships shows Erika is taller than Rachael, who in turn is taller than Tim. Since Tim is also taller than Joe, the complete order is Erika > Rachael > Tim > Joe, making Erika the tallest person among the group.