Your brain isn’t a muscle – in fact, it’s mostly fat – but the right kind of mental exercise can help keep it in shape. These puzzles are designed to give your problem-solving, reasoning, and concentration skills a workout. And they come in varying degrees of difficulty, so pace yourself!
How many times does the digit 5 occur in the numbers from 1 to 100?
Twenty times. The digit 5 appears 10 times as a last digit (5, 15, 25 … 95) and 10 times as a first digit (50, 51, 52 … 59).
The grid contains matches of different sizes, any of which may be completely unburned, partially burned, or completely burned. Matches burn from the head (the red end) to the tail without skipping segments. The numbers outside the grid indicate the number of burned segments in the corresponding row or column. Can you shade in the burned segments to ‘match’ the numbers?
Sophie and Caroline made arrangements to meet at a café at 2pm. Sophie thinks her watch is 25 minutes fast, although it is actually 10 minutes slow. Caroline thinks her watch is 10 minutes slow, while it is actually 5 minutes fast. What will happen if they both aim to arrive exactly on time?
Sophie will be 35 minutes late. Caroline will arrive at 1.45pm, 15 minutes ahead of time.
Space dust has landed on Earth, carrying with it seeds for exotic new alien flowers. One of them still lacks a name. If the xenobotanists follow the same rules they used to create the other terms, what should they call the last flower?
Cosmofilium jupibristo. The first half of the top term tells the colour of the flower’s centre; the last half is the petal colour. The first half of the bottom term tells the shape of the flower’s centre; the last half is the shape of the petals.
Place the words listed in the crossword grid.
A whole number between one and seven belongs in each of the seven bubbles. Each number occurs once. The sums of some of the numbers are revealed in the areas where their bubbles overlap. Can you figure out which number goes in each bubble?
None of the white squares in this diagram have their edges lined up. One of the squares is a different size from the others. Can you find it?
Carmela receives a text message from an unfamiliar number, so she texts back, “Who is this?”
The strange response: “It’s one of your female relatives. Your mother’s mother is my father’s mother-in-law.” Even assuming that this information is true, it doesn’t help Carmela pinpoint an individual, since there are two relationships it could describe. What are they?
Sister or first cousin.
Complete the grid so that each row, each column, and each three-by-three frame contains the 9 letters from the black box at the top. The hidden 9-letter word is in the diagonal from top left to bottom right.
Place the hexagons into the pyramid so each number is either greater than the sum of the two numbers below it or less than the difference between them. For instance, if two adjacent numbers were 20 and 50, any number higher than 70 or lower than 30 could be on top of them. (And no, do not turn 98 upside down to make it 86!)
Kate and Faizal both believe that they need a cup of coffee every three hours to stay awake and function. They both drink their first cup at 8am and another one every three hours thereafter until they go to sleep. Considering the following facts, who is spending more on coffee each week?
Kate stays up until 10pm Sunday through Thursday and until midnight on Friday and Saturday. Faizal stays up until 10pm every day.
Kate pays $3 per cup of coffee. Faizal drinks higher-grade organic coffee and pays $4 per cup.
Faizal. He spends $140 per week, while Kate spends $111
You just bought nine beautiful lakeside campsites, which you can rent to campers with tents for $20 per campsite per night. You can also upgrade the sites with electrical hookups. This will cost you $60 per campsite but will allow you to rent to RVers for $40 per night. Suppose you can always fill your campground to capacity. If you’re starting without any cash on hand, how many nights will pass before you’ll be able to upgrade all nine sites?
Three. On the first night, you’ll host nine tents and make $180, which you’ll use to upgrade three sites. On the second night, you’ll host three RVs and six tents, earning $240, letting you upgrade another four sites. On the third night, you’ll host seven RVs and two tents, earning you more than enough to upgrade the last two.
Rich lives in the Eastern Standard Time zone. His sister, Barbara, lives in the Central European Time zone, six hours ahead of him. Rich works between 8am and 5pm in his local time and goes to sleep each evening at 10 pm on the dot. Barbara works between 9am and 6pm and always goes to sleep at 11.30 pm in her own local time.
Is there any window in which Rich could call Barbara after his workday without interrupting her on the job or disturbing her sleep?
Yes, between 5 and 5.30pm EST.
Each letter from A through H has one of the 8 values listed below, and no two letters have the same value. Which number goes with which letter to make all the equations true?
2 3 4 5 8 12 13 17
F + A = C
G + B = D
F + D = H
B + H = C
E + G = B
A = 13, B = 5, C = 17, D = 8, E = 2, F = 4, G = 3, H = 12.
Place one of the four basic arithmetic operations (+, –, ×, ÷) in each box to make a correct equation. All operations are performed from left to right, ignoring the mathematical order of operations. The result at each step must be a positive whole number. What’s the equation?
5 + 7 ÷ 3 × 9 – 4 = 32
The playing card suits in the cells above are placed according to a pattern. What’s the missing symbol?
Spade. Each suit has a numerical value: diamonds equal one, hearts equal two, spades equal three, and clubs equal four. Or, if you prefer, diamonds equal four, hearts equal three, spades equal two, and clubs equal one. Either way, each row and column adds up to 10, and the missing symbol is a spade.
How many pets live in my house if all of them are snakes except two, all are hamsters except two, and all are rabbits except two?
One of each, for a total of three.
The Reds, the Greys, the Blues, and the Blacks have a round-robin tournament where each team plays the other teams once, for a total of six games. The Blacks won more games than the Blues, and the Greys lost more games than the Blues. The Reds tied the Blacks, the only tie in the tournament (a tie counts as neither a win nor a loss). Who won the game of the Reds versus the Blues?
The Reds. The Blacks tied one game, so they won a maximum of two games. They won more than the Blues, so the Blues won a maximum of one game. Since the Greys lost more times than the Blues, the Greys must have lost all three matches. The match that the Blues won must have been against the Greys, so the Blues lost the match against the Reds.
Lois and Helen, widowed sisters, lived together in the country. Their habits never changed: up at dawn, breakfast, some housework and gardening until lunch. In the afternoon, Helen napped while Lois watched her shows – Helen never watched TV. Then Helen would clean the vegetables for dinner and Lois would cook. In the evening, they’d read before bed. One night before they turned in, a storm knocked out the power. Everything was pitch-black, and Lois began to panic. “What should we do?” she cried. Helen just smiled and kept reading. Why did Helen stay calm while her sister did not?
Helen was blind.
Jacob enjoys steak so much that the probability that he’ll have it for dinner on any given evening is one in three. The favourite dish of his wife, Patricia, is fresh fish. The probability that she’ll have it for dinner on any given evening is one in two. Because Jacob and Patricia always dine together, they’ll never have steak and fish on the same night. On average, how many times in a 30-day month will they be eating either steak or fish?
Each of the three lines of letters below spells the name of a fruit, but four letters from the first word are in the third line, four letters from the third word are in the second line, and four letters from the second word are in the first line. What are the words?