Now imagine that this cube is divided into 27 one-inch cubes. The maximum number of cubes visible to an observer at any one moment is With a 4 X 4 x 4 cube further subdivided into 64 cubes, the maximum number of cubes that can be seen by an observer at any one moment is How many cubes can be observed in a 5 X 5 X 5 cube smaller cubes total and a 6 X 6 X 6 cube smaller cubes total?

### Blog Archive

No humans are not mammals. No mammals live on Mamal. Adam Mammale, a former pilot who once lived in Detroit, can live only on Mamal. Hint: Only a certain p e r c e n t a g e will solve this. M i Fill in the letters to complete the following word, which means "fulfilled, achieved. Here's a different twist on a c u b e puzzle. The diagram shows six connected squares that need to be folded into a cube.

Next to t h e squares are four views of t h e same cube. Can you fill in the six squares with the appropriate figures? Chordorfs are less numerous than chlordorfs. Chlorodorfs are more numerous than chlordorfs. Chloroodorfs are less numerous than chlordorfs. If you were to list the most numerous of the preceding four items, from the top down, where would chloroodorfs fit?

What the closest possible relationship 1 can have to Joseph? Which ones are incorrect? No fair using plurals. Bob has threefourths of Pete's share of the remaining candy. What fraction of the total n u m b e r of pieces of candy does Pete have? The following words can all be transformed into new words by prefixing the same three letters, in the same order, at t h e beginning of the words. What are the three letters? The first n u m b e r is not 1, and the second, third, and fourth n u m b e r s must increase in value.

We'll give you o n e answer, but t h e r e ' s another. Hint: Get p r i m e d for this puzzle. Determine t h e relationships b e t w e e n t h e pictures and the letters to find t h e solutions:. Can you find a similar relationship b e t w e e n t h e w o r d s double and stationary that will form a new w o r d in t h e blank? From t h e following rules, can y o u find a solution? Here is a five-letter "trickle-down" puzzle. Change o n e letter at a time to reach t h e final word. There are 6 O in an I.

You are taking a long drink of water. Which happens first? What is t h e missing letter in t h e last triangle? They played for a pizza at each match, but no pizzas were purchased until the end of the week. If at any time during the week Tom and Bill had the same number of wins, those pizzas were canceled. Bill won four, matches but no pizzas , and Tom won three pizzas.

How many rounds of golf were played? What relation is Susan to Judy and Mary? By straight, I mean that they can be separated by consonants, but not by another vowel. A professional bass fisherman caught 30 bass during a five-day tournament. Each day, he caught three more fish than the day before. How many fish did he catch the first day? Here's an alphametic puzzle that isn't t o o difficult. See ij you can replace the letters with the p r o p e r numbers to make this puzzle work.

The smaller boxer is an amateur and also the son of the bigger boxer, who is a professional. But the pro boxer is not the amateur's father. Who is the pro. Find the other two ways. No diagonal cuts or rotations allowed for example, 1 turned 90 degrees doesn't count. A friend who is quick with probabilities advises you against making this bet.

Which is the odd one out and why? There are only t h r e e palindromic squares under 1, What is the third palindromic square under 1,? What is the first palindromic square over 1,? Part of a basketball team stopped by a restaurant and ordered nachos. How many team m e m b e r s were originally in t h e restaurant? Hint: Don't u s e 5 or 7. T h e letters of t h e word vile can be rearranged to live, evil, and veil. Try to find a four-letter word that can be c h a n g e d into four new w o r d s five total, counting your original.

## Full text of "The Colossal Book of Short Puzzles and Problems"

See if you can decip h e r t h e word. How big is angle X? By playing with t h e letters of e a c h word, s e e if you can determine t h e trait. Each d o c t o r is either a surgeon or a dermatologist. At least o n e is a dermatologist. Hint: Think of a musical. How much did the round of golf cost cart included, of course! If two gallons of paint are needed to cover all sides of one cube, how many gallons are needed to cover all exposed surfaces of t h e figure below? Include surfaces on which the figure is resting. Hint: There are no hidden cubes.

You may use any math symbol or sign you wish. Remember, only t h e n u m b e r 4 may be used and only twice. What is t h e weight of t h e whole block of chocolate? As t h e s t o r y goes, a f o r t u n e teller had put a curse on him that h e would lose every time h e played roulette. F 0 r t h e ten y e a r s since, he has b e e n losing consistently every day, yet h e is a v e r y wealthy m a n w h o has a loving wife and family. How could this family b e so wealthy?

I Six hours ago, it was two hours later than three hours before midnight. What time is it? Many of the distributors want another cutting in between these two offerings. Fair enough, right? Where would you buy your gems, or does it even make a difference? What are the next two numbers in t h e following sequence and why? Consider only the first nine numbers. The box pictured here has been folded together from one of four choices below. Which is t h e correct one? Complete the s e q u e n c e by filling in the remaining numbers.

How is the pattern formed? W Maria covered the first half of a bicycle race at 20 miles per hour. The second half of the race was a return over the same route, and her return s p e e d was 30 miles per hour. What was Maria's average s p e e d for the entire trip? Take your time with this. If h o u s e number 12 is opposite h o u s e number 29, how many houses are there on both sides of t h e street?

SI One of the five following figures does not belong with the rest. Which one is it, and why? On its return, it travels at 10 mph. The trip downstream is three hours shorter than t h e trip upstream. How far is it from the beginning of the trip to the turnaround point downstream? SI If Alicia is three times as old as Amy will be when Alex is as old as Alicia is now and Alex's age is a square number, who is t h e second oldest?

Can you give their ages now? What letter word is written in t h e block below? Start with a n y letter and move o n e letter at a time, in any direction, but d o n ' t go back over a n y letter! Hint: Think outside t h e boxes. Is t h e r e a statement that can be m a d e for certain about t h e proportion of pitchers among left-handers c o m p a r e d to all ballplayers?

Is it greater, smaller, or the same, or is t h e r e not enough information to tell? What is t h e relationship among t h e circles, squares, and dividing line that determines t h e respective numbers? What n u m b e r goes with t h e sixth figure? Draw a square. Now divide the square into four equal, congruent p a r t s with three straight lines. None of the lines may cross each other within the square. Hint: Think Roman. The dreaded cube-eaters from the fourth dimension d e s c e n d upon a stack of 27 identical sugar cubes. Cubeeaters can only eat to the center of a cube. When they reach the center, they always make a 90 turn and proceed to the next cube.

They never reenter a cube. If a cube-eater enters at location A, what is the minimum number of cubes it will eat through to reach the cube at location B? Based on the given scores only, see if you can figure out who would win and by how much if Harvard were to play Montana during this season. Assume that all rows and columns are complete unless you actually see them end.

Given the following information, determine which flowers grow where. The Smiths do not grow violets. The Morgans grow peonies; they do not live on 2nd Street. The Parks live on 3rd Street. Begonias bloom on 4th Street. Roses do not grow on 5th Street. The Johnsons do not live on 1st Street. The Rosens do not grow daffodils.

The Johnsons grow roses. Daffodils grow on 1st Street. Place the queens on t o p of t h e kings facedown in one stack. Pick up the stack, and starting with the t o p card queen , place it faceup on a table. Take the second card and place it facedown on t h e bottom of the cards in your hand; place the third card faceup on the table, t h e fourth card on the bottom, and so on, until all cards are faceup.

What is the order of t h e cards that are faceup? There are 14 D in a F. H See if you can unscramble the following words to make a sensible sentence out of them. Here's another "trickle-down" puzzle. Change one letter on each line to reach the final word. There may be more than one way to do this puzzle. What is the maximum number of bounded areas that result when six circles are intersected? Assume that the first three statements are true and then determine whether the fourth statement, the conclusion, is valid or false.

That's all there is to it! Some zers are tifs. All tifs are xorts. Some xorts are wots. Therefore, some zers are definitely wols. Of course, there are others.

### Search form

Here's a new twist. Can you make at least one nine-letter word from those same letters? You may use any of the letters more than once. See if you can determine whether the argument is valid or invalid. If we are to survive and prosper as a species, solving the riddles of the universe via mathematics becomes the single most important focus of theoreticians.

Thus, only the most brilliant minds will succeed. Another glass, exactly the same size, is one-seventh full of the blue dye. Each glass is then filled to the top with water and their contents mixed together in a large container. What proportion of this final mixture is blue dye and what proportion is water? One of the figures shown here lacks a characteristic common to the other five. Which figure is it, and why? The last letter, R, is placed outside the grid of the other letters.

Using each letter only once, and beginning with the first letter of the word, which may be in any of the nine positions of the grid, spell the word by moving up, down, sideways, or diagonally to adjacent letters. The relationships are the same for all four boxes. What is the missing number? This next sequence puzzle is math related, but not exactly what you might think at first.

Fill in the missing term. Hint 1: Think leap year. Hint 2: Be careful! Some calculators will give you the wrong answer.

How many total cubes are there? Given the information below, can you determine who is married to whom and the color of their house? One of the houses is red. Harry does not live in the white house. Alice is not married to Brad. Steve lives in the yellow house. John is not married to June. Harry does not live in the blue house. Alice lives in the blue house. June is married to Harry. Nancy is not married to Steve.

Sara is one of the wives. There are 24 K in P G. Timer Spool Reward Emit Diaper Desserts i See if you can ascertain the nature of the relationship among the pictures in each row in order to fill in the missing figure in row 3. I am six times as old as my sister. In one year I will be five times as old as my sister will be.

In six years I will be three times as old as my sister will be. How old am I and how old is my sister? Can you identify what that characteristic and its reverse is? I Sometimes people wonder whether puzzles have any reallife applications. You be the judge. Here's an example: A mother was throwing a birthday party for her daughter and realized that, with only nine s c o o p s of ice cream, there wasn't enough to give two s c o o p s to each of the five children present.

She quickly came up with an idea that pleased alland everyone got an equal amount of ice cream.

By the way, she did not divide the s c o o p s into fractional portions. How did this real-life mom solve her dilemma? Fred, a football fanatic, is going to his first University of Nebraska football game. He doesn't know that Nebraska has the nation's longest streak of consecutive sellouts for their home games. See if you can find the number of people that were sitting in the north end zone with Fred.

Each letter in the following alphametic retains the same value within the problem, and the value must be different from that of any other letter. Zero may not begin a word. The first four are newly created English words that are related to their respective patterns. For the fifth pattern, you have to come up with the word; for the last word, you have to come up with the pattern.

In alternating turns, each player picks up at least one, but not more than five pennies per turn.

## The Penguine Book of Curious and Interesting Puzzles

The player who picks up the last penny wins. However, the penny has to be the only one left for that player to win. In other words, if your opponent picks up five pennies, you can't pick up four and call yourself the winner. Under these guidelines, if you go first, is there a move you can make to ensure that you win?

His problem is that he must have an odd number of snakes in each cage. How can he accomplish this? You can put any number of snakes in a cage as long as the total number of snakes in each cage is an odd number. Fifteen of the dealers have fewer than five such cards to trade, 11 others have more than six of them to trade, and three others have more than s e v e n to trade or sell.

What is the total number of dealers that have five, six, or seven Mickey Mantle cards? Fill in the missing term in this mathematical series. Hint: This is not a particularly common phrase, but it's solvable. Think "game. After six miles, the wind blew his hat into the stream. Thinking that he had no chance to recover his hat, he continued upstream for six more miles before turning back.

He continued rowing at the same rate on his return trip and overtook his hat at exactly the same spot where he began his journey, eight hours earlier. What was the velocity of the stream? What is the fewest number of lines that would need to be erased to do away with all of the triangles in this figure? He found he could walk the length of the walkway, moving in its forward direction, in one minute.

Walking at the same rate against the forward direction of the walkway, it took him three minutes to cover the same distance. He wondered how long it would take him to cover one length if the walkway were to stop. Can you help him out? This may not be as easy as it first appears. You may use any mathematical symbols or signs you wish, with the exception of infinity oc and ellipses You may not use any of the three nines together in combination, such as 99 x 9. In other words, each nine must remain by itself before any math operation is performed on it. Additionally, no mathematical symbol or sign may be used more than four times.

What is the smallest number of pieces of candy the box can contain? Start w'th any letter and move one letter at a time, in any direct n b. Hint: Tackling this puzzle head-on won't help you. Try different directions. Try your luck at this "trickle-down" puzzle. Remember, change one letter at a time to arrive at the answer.

Construct a chart to consider the possible values. E cannot equal zero since that would make N zero. We need a value where four E's equal N and four N's are equal to E plus a carryover. From the chart, we see that the only place where that occurs is when E equals 2. When referring to columns, they are numbered from left to right. Therefore, the greatest number of the three could be a 6 with no carryover from the second column, or a 5 with a carryover from the second column. Obviously, there is a carryover from, or to, at least one of the two middle columns, since their sums yield two different letters.

Let's make an assumption that there is a carryover to the first column, and, therefore, no number can be greater than 5 in that column. Therefore, N equals 2 and E equals 6. If N is 2, then O must be 4. Since we accounted for the numbers 2, 3, and 4. Here are three solutions. Can you find others? View C is not correct. Besides the three shown in this puzzle, eight other ways are possible.

It is always helpful to set up a legend of what is given and to work from there. Multiply the first equation by -. In this case, Z can only equal 5. With any greater number, Y will become a negative number. As you can see, there are only three possibilities where a chocolate cupcake could be chosen first. If the first digit of the four-digit code cannot be 0, 5, or 7, that leaves seven possible numbers for the first digit. All ten digits, however, can be used for the second, third, and fourth numbers.

Columns are numbered from left to right. There has to be a carryover of 2 to the first column. If P were 9 and Q were 8, with a carryover of 1 from the last column, the sum of 20 could not be reached if R equaled 1. Therefore, R cannot be 1. The powers of 7 have a repeating pattern for the last digit that can be found easily without performing the entire multiplication of each power.

Then 7 would be in the next column, 7. Its remainder is 7 when divided by This type of puzzle is a form of syllogism. It can best be shown by using Venn diagrams. Case 1 Case 2 From Case 1, we can see that it is possible for a Cornhusker to be a Cyclone fan, but from Case 2, it is not definite.

The conclusion is false. Obviously, their number system is based on something other thai Let's say it is based on a notation represented by N. Their number system is then BASEg and 5 x 4 x 7 , our , becomes their Since Dave spoke to the biologist, and Ann was sitting next to the chemist and across from the doctor, Cathy must be the author, and Ann is the biologist.

The doctor didn't speak, but Dave did. So, Boobie is the doctor and was thinking of her own parents and Dave is the chemist. Turn the first grid 90 to the right, and delete the bottom row of figures. Then turn the result 90 to the right again and delete the. Do the same with the third grid to get the answer. One of the first things you may have noticed is that the horizontal figures both contain an L, whereas the two vertical figures contain an R.

The equations with two figures both contain a B and the equations with three figures both have a G. The circles have an A and the diamonds an E for their lone vowels. So, that yields this basic information. In the first two foreign phrases, roi is the only common word. The word "three" in the English version is likewise the only common word; so, roi means "three. The English translations share the word meaning "coins.

Comparing the first and third phrases, we see they share the word kaf, meaning "take. The probability is Twenty-two percent of the peopi e are not gum chewers and 65 percent are over fifteen years old. Therefore, 22 percent x 65 percent or The only relationship these capital letters have is that their shapes are totally or partially closed.

R is the next and last letter of the alphabet that meets this requirement. The answer is "A is larger than B by 1. It only took John four steps to accomplish his task. Step 1John filled the five-gallon bucket and poured all of it into the six-gallon bucket. Step 2He refilled the five-gallon bucket and poured out one gallon into the six-gallon bucket to fill it, leaving four gallons in the five-gallon bucket.

Step 3He dumped the six-gallon bucket and poured the four gallons from the five-gallon bucket into the six-gallon bucket. Step 4Then, John refilled the five-gallon bucket and started home for a piece of cake. The answer is These four numbers read the same right side up as they do upside down.

## Knowledge puzzles

The numbers on the right are the ones that most closely follow the ones on the left. The next number is 4. Here's how to set up the problem. If the difference of the numbers of the series is taken to the end, a pattern of - 3 is established. The next number in the series must yield a - 3 in the bottom row. The number next to - 8 must be In one day, nine men work at a rate of X compared to seven women who work at a rate of Y. The women are better workers by a ratio of 17 to 9. The next number is Notice that no digit is greater than 4. The missing number is 1. The number is 8.

Starting with the first and last numbers and working towards the middle, each pair of numbers totals This is actually two different series contained within one. One series begins with 0 and continues with every other number. Likewise, starting with the 2, a second series is established with every other number. The missing number is 5. In this problem, the differences between the n uinbers forms a pattern, allowing you to predict the next numbers.

After finding the difference, find the difference of the resulting numbers. The correct number is These numbers represent the answers for each of the six problems starting with Puzzle The maximum number of cubes is nineteen. There are several different methods of approaching this problem. Since there are three unknowns, it is helpful to establish whatever relationship may exist between the unknowns and then attempt to express that relationship in common terms.

From several thousand feet high, the pyramid would look like this The 60 angle between Lines A and B would appear to be 90 to Judy. Think of the two figures as an opaque rectangle that has an opaque square behind it. To arrive at the second part of the analogy, the square the bottom figure rotates 45 in either direction, and the rectangle the top figure rotates 90 in either direction.

To find the correct solution, rotate the rectangle now the bottom figure 45, and rotate the square now the top figure The answer is C. Consider the first figure in the analogy to be two t r a n s p a r e n t triangles sharing a common base. Let the triangle on the left flip downwards, using the base as an axis. Likewise, in the third figure, let the line connected to the circ on the left fall around the base.

C is the answer. A cube is made up of six planes; a tetrahedron has four planes. A tr iangle has three planes, so it needs two lines to keep it in the same g to 4 3 to 2 ratio. Only A works. In the first two figures of the analogy, place the vertical line of the s e cond figure directly behind the vertical line of the first. Where two dags meet on the same side of the line, they turn into a square on the third figure.

Where a flag and a circle meet, they cancel each other out. Forgot your password? Or sign in with one of these services. This topic is now archived and is closed to further replies. Please be aware that the content of this thread may be outdated and no longer applicable. I will try to make this as clear as I possibly can. Before you even attempt this puzzle, you must first complete the Cyclum puzzle. Complete it to get a tragic torch, which will light up the first part of this new puzzle.

There, you will find that the left side is lit up by a torch. There is also a console on the left. When you click the console, it will take you to a dashboard. There will be characters on the bottom, as well as a black and gold string of symbols on top. To progress with the puzzle, you need to exchange codes. They will input the opposite code of yours black or gold. When they input yours, the gaps will turn purple. After that, you can move on to the second part. But make sure you keep in touch with your buddy, because you'll need them for the second part.

By now, the other half of the first screen should be lit by a second torch. There is a second console. When you click on the console, you'll either have tile squares and a string of black symbols at the top, or vice versa. There are 32 symbols and 13 tiles. One partner will get the symbols and the other will get the tiles. I happened to get the tiles, so my screen looked like this:. Now comes the hard part. You need to put in the code that your partner has, as well as give them the code that you received on yours. As far as I can tell, it's random, and the symbols never correspond to the same tiles twice.

Usually, when you swap codes, at least one dot will light up. For example, let's say that I have a tile with a dash at the top. My partner has a symbol that looks like a funky F. We happened to find, through trial and error removing the tiles and submitting until something turned off , that the F symbol and the tile make one of the dots light up when they're in a certain slot.

It is Ellen's hope that her dedication to these books will bring you and your family hours of fun, challenges, and even some laughs. Ellen plans to continually update her series with new editions, so you will always have a delightful variety of brain challenging puzzles to try. A delightful variety of brain challenging puzzles, from easy to more difficult levels.

Complete instructions are included for each puzzle, with detailed picture examples. While you are having fun solving the puzzles and laughing at the famous quotes, your brain is being exercised, too. This helps to improve memory, logic skills, concentration and vocabulary. Read more Read less. No customer reviews. Share your thoughts with other customers. Write a customer review.