Long places ten black marbles in a circle, then inserts a white marble between each neighboring pair of black marbles. Finally he puts a blue marble between each adjacent black and white marble. How many blue marbles are there?
Jerry writes a number. Tom multiplies it by $3$, Spike adds $3$, Mickey divides by $3$, and Donald subtracts $3$ to obtain $8$. What was Jerry’s number?
Tien and Son have equal amounts of money. Tien buys three pencils and four notebooks with $7$ dollars left; Son buys three pencils and three notebooks with $28$ dollars left. What does a notebook cost?
Five boys say: $A$: “$B$ tells the truth”; $B$: “$C$ lies”; $C$: “$D$ tells the truth”; $D$: “$E$ lies”; $E$: “I tell the truth”. $E$ is incorrect. How many tell the truth?
An and Binh each buy the same toy. An pays with sixty $2$-dollar notes. Binh uses equal numbers of $1 - , 2$- and $5$-dollar notes. How many notes does Binh use?
Nhi forms $2021$ with matchsticks. Move exactly two sticks, without adding or removing any, to make the greatest four-digit number using the displayed digit patterns. What number is it?
Replace $\triangle$ and $\blacksquare$ with +, −, $\times$ or $\div$ so that $12\triangle4+10\blacksquare2=23$. Using those operations, evaluate $12\triangle2+10\blacksquare4$.
A machine halves an even input and subtracts $1$ from an odd input, repeating until $0$. Find the smallest number requiring exactly six steps. For example, $3$ → $2$ → $1$ → $0$ takes three steps.
Ten coins start face down. Flip one coin in round $1$, three in round $2$, five in round $3$ and seven in round $4$, after which all face up. At most how many coins are flipped three times?