With one straight cut, snip a small triangle off one corner of a square. The cut crosses the two sides that meet at that corner. How many corners does the bigger piece have now?
Good to know: The cut crosses each of the two sides partway along, not through another corner, and only the bigger piece's corners are counted.
Hint 1
Draw a square on paper and try it with one pencil line.
Hint 2 (more help)
Count the corner the cut takes away, then the new corners it makes where it crosses each side.
Reveal the answer
Five.
A square has 4 corners. The cut takes away 1 corner, leaving 3. But it makes 2 new corners, one where it crosses each side. 3 + 2 = 5, so the bigger piece is a pentagon, a shape with five corners.
A snail climbs 3 meters each day and slips 2 meters each night. Starting at the bottom, on which day does it first reach the top of a 10-meter wall?
Good to know: The snail starts at the bottom in the morning, climbs 3 meters every day and slips 2 meters every night. Once it reaches the top, it stops and does not slip.
Hint 1
Each day and night together, the snail ends up only 1 meter higher. But watch the very last day.
Hint 2 (more help)
On its last day, the snail can reach the top before night comes, so it never slips back.
Reveal the answer
Day eight. It reaches the top that day, so it never slips back down.
After each day and night, the snail is 1 meter higher: at 1 meter after the first night, 2 meters after the second, and 7 meters after the seventh. On day 8 it climbs 3 meters, from 7 to 10, and reaches the top before night. The quick answer, day 10, forgets that last big climb.
Two US coins total 30 cents. One of them is not a nickel. Which coins are they?
Good to know: Only real US coins count. "One of them is not a nickel" is true of the quarter; it does not mean the other coin cannot be a nickel.
Hint 1
List the coins that could add up to exactly 30 cents with just two of them.
Hint 2 (more help)
The riddle says one coin is not a nickel. It does not say that neither coin is a nickel.
Reveal the answer
A quarter and a nickel. The quarter is the one that is not a nickel.
The only two US coins that make 30 cents are a quarter (25 cents) and a nickel (5 cents). The riddle says one of them is not a nickel, and that is true: the quarter is not a nickel. The other coin is.
A bat and a ball cost $1.10 altogether. The bat costs $1 more than the ball. What does the ball cost?
Good to know: The bat and the ball are the only two things, and the prices are in whole cents.
Hint 1
Test your first guess: add the ball's price and the bat's price. Is the total $1.10, and is the bat exactly $1 more?
Hint 2 (more help)
If the ball were 10 cents, the bat would be $1.10, and together they would be $1.20. Try a smaller amount.
Reveal the answer
Five cents. The bat costs $1.05.
If the ball costs 5 cents, the bat costs $1 more: $1.05. Together, $1.05 + $0.05 = $1.10. The quick answer, 10 cents, does not work: the bat would cost $1.10, and the total would be $1.20.
A farmer must take a fox, a chicken, and grain across a river. The boat carries the farmer and one item. Without the farmer, the fox cannot stay with the chicken, or the chicken with the grain. How can everything cross?
Good to know: Only the farmer can row the boat, and it holds the farmer plus at most one item. Trouble happens only on a bank the farmer has left, never during a crossing.
Hint 1
Which one is the troublemaker that cannot be left with either of the others?
Hint 2 (more help)
The boat can carry something back to the start, too.
Reveal the answer
Take the chicken across. Go back alone. Take the fox across. Bring the chicken back. Take the grain across. Go back alone. Take the chicken across.
The chicken is the problem: it cannot be left with the fox or with the grain, so it crosses first. Then the farmer takes the fox over, brings the chicken back, swaps it for the grain, and fetches the chicken last. Taking the grain before the fox works too. Seven trips is the fewest possible.
Anna, Beth, and Cara each have a different pet: cat, dog, or fish. Anna has neither cat nor dog. Beth does not have the dog. Who has each pet?
Good to know: Each girl has exactly one pet, and no two girls have the same kind of pet.
Hint 1
Start with the person the riddle tells you the most about.
Hint 2 (more help)
Anna has neither the cat nor the dog, so only one pet is left for her.
Reveal the answer
Anna has the fish, Beth has the cat, and Cara has the dog.
Anna has neither the cat nor the dog, so she has the fish. Beth does not have the dog, and the fish is taken, so Beth has the cat. That leaves the dog for Cara.
Eight balls look identical, but one is heavier. Using a balance scale, how can you always find it in no more than two weighings?
Good to know: Exactly one ball is heavier, and the other seven weigh the same. The balance scale only shows which side is heavier, or that the two sides are equal.
Hint 1
Think about splitting them into more than two groups.
Hint 2 (more help)
Put 3 on each side for the first weighing. What can each result tell you?
Reveal the answer
Weigh three against three. If they balance, weigh the last two against each other. If one side is heavier, take two balls from that side and weigh one against the other; if they balance, the third ball from that side is the heavy one.
Weighing 3 against 3 splits the eight balls into three groups: one pan, the other pan, and the 2 set aside. If the scale balances, the heavy ball is one of the 2 set aside, and one more weighing finds it. If one side is heavier, the heavy ball is one of those 3: weigh 1 against 1, and if they balance, it is the third. Either way, two weighings are enough.
In a three-digit number, the tens digit is two more than the ones digit. The hundreds digit is one less than the tens digit. The digits add to 12. What is the number?
Hint 1
Call the ones digit a mystery number, then write the other two digits using it.
Hint 2 (more help)
The hundreds digit is one more than the ones digit. Try ones digits 1, 2, 3 and add up all three digits each time.
Reveal the answer
453.
If the ones digit is 3, the tens digit is 5 (two more) and the hundreds digit is 4 (one less than 5). 4 + 5 + 3 = 12, so the number is 453. Other choices miss: a ones digit of 2 gives 342, whose digits add up to only 9.
A drawer has three red socks and three blue socks. Without looking, how many socks must you take out to be sure of getting two of the same color?
Good to know: You take socks out one at a time without looking, and any two socks of the same color count as a pair.
Hint 1
Think about the unluckiest way the socks could come out.
Hint 2 (more help)
Your first two socks might be one red and one blue. What about the next sock?
Reveal the answer
Three.
The first two socks might not match: one red and one blue. The third sock has to be red or blue, so it always matches one of them. Three socks are always enough, and two are not.
A pen holds only chickens and rabbits. There are 20 heads and 56 legs. How many rabbits are there?
Good to know: Every chicken has 2 legs, every rabbit has 4 legs, and each animal has one head.
Hint 1
Every animal has one head, so there are 20 animals in all.
Hint 2 (more help)
If all 20 were chickens, there would be 40 legs. Each rabbit has 2 more legs than a chicken.
Reveal the answer
Eight rabbits and twelve chickens.
Pretend all 20 animals are chickens: that makes 40 legs. There are 56 legs, which is 16 more. Each rabbit has 2 more legs than a chicken, so 16 ÷ 2 = 8 rabbits. The other 12 are chickens. Check: 8 × 4 + 12 × 2 = 32 + 24 = 56 legs.