You have a string-like fuse that burns in exactly one minute. The fuse is inhomogeneous, it may burn slowly, then quickly, then slowly, and so on. You have a match and no watch. How can you measure exactly 30 seconds?

"String-like" why is that helpful to this situation?

60 seconds divided by two is...?

Bend the fuse so that you can light both ends simultaneously.

If you light both ends simultaneously you will be cutting the total burn time in half.

You receive eight balls. They are identical except that one is heavier than the rest. You have access to a scale but it cost $10 per use. What is the least amount you can spend to find which ball is the heaviest and how?

Don't think in pairs.

Groups of three?

$20

You must use the scale two times. You can separate the balls into three groups : three balls, three balls, and two balls. You start by weighing the sets of three against each other. If these are equal then they must be identical in weight. The heavy ball must be in the group of two. Put them on the scale and see which is heaviest. In the other scenario where one group of three is heavier than the other, you have identified which group the heavy ball is in. Choose two balls out of the group and use the scale. If one is heavier then that is your ball, if they are identical then the heavy ball must be the one not weighed.

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly? Which box should you choose from?

A key piece of information is that all of the boxes start mis-labeled

Draw the boxes and the labels out, then try starting which each box

You must pick from the box labeled "Apples and Oranges" - then you will be able to determine the correct labeling.

You know the labels are incorrect so the box labeled "Apples and Oranges" must be either all apples or oranges. Suppose you remove an orange, the box must therefore be all oranges. You now have two labels left: "Apples" & "Apples and Oranges". Also remaining are two incorrectly labeled boxes: "Oranges" & "Apples". Since the "Apples" label can't go on the box already labeled "Apples" you know this one must be "Apples and Oranges". You now have one box and one label so by process of elimination you can correctly label the last box "Apples".

A snail is climbing a 10-foot flag pole. He climbs up three feet every 45 minutes. He likes to take naps for 15 minutes after climbing. While sleeping, he slides down by one foot. How long until he reaches the top of the pole?

Don't take shortcuts

Draw it out

Four hours and forty minutes

The quick answer is to establish that the snail climbs a net of 2 feet per hour, reaching the top in 5 hours. Yet, you can't forget about the max height of each hour. The snail's max height is always 1 foot higher than where he slides down to by the end of the hour.

You're trying to crack a three-number dial safe. Without knowing the combination numbers, what is the maximum number of trials required to open the safe? A trial is considered a full three-number combination. There are 40 numbers on this safe. To enter a combination you start with the dial at zero and turn counter-clockwise until the first number, then clockwise back to zero, then clockwise to the second number, then counter-clockwise back to zero, and finally counter-clockwise to the third number. Upon the correct combination, the safe will spring open.

64,000 and you've spun out of control.

How many numbers of a combination do you truly need?

1,600 trials

The quick answer is generally 40 to the third power, 64,000. This number can be reduced greatly. If you input the first two numbers correctly you don't need the third, you only need to turn the dial through the numbers until the safe springs open. This brings the answer down to 40 to the second power, or 1,600.

What is the angle (if any) between the hour and minute hands of a clock when the time is 9:45?

Try drawing this out the best you can. Make sure your answer stays logical.

One hour is one-twelfth of the full circle and 45min is three-quarters of one hour.

22.5 Degrees

If the time is 45 minutes into the hour then the hour hand must be three-quarters of the way to the next hour. A full circle is 360 degrees and a clock is a circle divided into 12 hours. The distance between each hour is one-twelfth of a circle, 30 degrees. If the minute hand is pointed at the nine and the hour hand is three-quarters to the ten then the answer becomes three-quarters of 30 degrees, 22.5 degrees.

You start with a single lily pad sitting on an otherwise empty pond. You are told that the surface area of the lily doubles every day and that it will take 30 days for the single lily to cover the surface of the pond. | If instead of one lily pad you start with eight lily pads (each identical in characteristics to the original lily), how many days will it take for the surface of the pond to be covered? Assume that they don't overlap each other.

If your answer is 3.75 days (30 divided by eight) then you should try again.

How many days for a single lily to be equal to eight lilies?

27 days

If the eight lilies are identical in nature to the single lily then you can think of the eight lily pads as one big lily pad. The question then becomes how many days for one lily to become equivalent to eight lilies. You can subtract this time saved from 30 days. It takes three days for a single lily to grow to the equivalent of eight lilies. So you can shave three days off of 30.

Your sock drawer contains 11 red socks and 15 blue socks. Your light isn't working and you must select your socks without seeing them. What is the minimum number of socks you need to take from your drawer and carry to a well-lit room to guarantee at least a matching pair?

Try thinking about this very vividly and walk through the process.

How many socks make a pair?

Three socks must be chosen.

The answers and justifications I've heard for this question are why I love logic questions. The answer is three - the first two socks can be different but the third MUST match one of the first two, giving you a matching pair.

Picture a 10 x 10 x 10 "macro-cube" floating. The macro-cube is composed of 1 x 1 x 1 "micro-cubes", all stuck together. Through some damage, the exposed (outermost) layer of micro-cubes loosen and fall to the ground. How many micro-cubes are on the ground?

Most people start by counting 1 x 1 micro-cubes on each face and adding them up. This is a much more difficult and error prone approach than necessary.

Think volume instead of independent micro-cubes

488 micro-cubes are on the floor

There is a macro-cube and then after a layer falls off, a smaller macro-cube. The answer is then the difference in volume between the cube in its first state and the volume of the cube after a layer falls off. The volume of a cube with length n is n^3. The answer then becomes (10^3) - (8^3). A common mistake is to take (10^3) - (9^3).

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

Can you send the 2 slowest people together?

What if person 1 waits?

17 minutes

Most people initially respond with the idea to use the fastest person as an usher, taking everyone across in 21 minutes. But that's just too easy and we can do better. It's best to have the two slowest people cross together. The only way to do this without having a slow person cross twice is to have someone waiting on the other side when they arrive
1 and 2 cross Time: 2 minutes 2 comes back Time: 4 minutes 7 and 10 go across Time: 14 minutes 1 comes back Time: 15 minutes 1 and 2 go across Time: 17 minutes

What is the sum of integers from 1 to 100? Integers are whole numbers only.

What do the first and last number add up to?

What do the second and second to last number add up to? Do you sense a pattern?

Sticking with the above pattern the third and third-to-last also add to 101. Continuing with this you will find 50 pairs of 101; which when summed equals 5050. Ultimately you can turn this into an equation that can be applied to any similar question of 1 to n by doing n/2 *(n+1)