Using 6 matchsticks, we can make just one rectangle measuring 1 × 2, as shown below.
What is the greatest number of rectangles measuring 1 × 2 that we can make with 14 matchsticks?
Michael chooses a natural number, multiplies it by itself, adds 1, multiplies the result by 10, and adds 3. Finally, he multiplies the result by 4 and obtains 2012. Which number did Michael choose?
Borya the rabbit loves cabbages and carrots. In one day, he can eat 9 carrots, or 2 cabbages, or 1 cabbage together with 4 carrots. In one week, Borya ate 30 carrots. How many cabbages did he eat that week?
Alice enters the world through the looking glass. This time, she has turned back time to save the Mad Hatter. The White Queen warns her: “If you do not put the metal sphere back into the machine before the minute and hour hands coincide, everything will be destroyed.” The clock now shows exactly 5 o’clock. How much time does Alice have to save the Mad Hatter before everything is destroyed? Let us answer the following questions to find the solution!
1. In one hour, how many complete turns does the minute hand make, and how many does the hour hand make? How many more turns does the minute hand make than the hour hand in each hour?
2. At 5 o’clock, which numbers do the hour and minute hands point to, respectively? At 5 o’clock, how many turns ahead of the minute hand is the hour hand?
3. From 5 o’clock until the hands first coincide, how many more turns does the minute hand make than the hour hand?
4. Using your answers above, calculate the shortest time after 5 o’clock until the minute and hour hands coincide. Thus, how much time does Alice have to save the Mad Hatter?
The number 35 has the property that it is divisible by its units digit (35 = 5×7). However, 38 does not have this property. How many numbers greater than 21 and less than 30 have this property?
On a die, the numbers of dots on any two opposite faces always add up to 7. Four dice are joined together as shown.
Which picture shows what they look like from behind?
The diagram shows roads between the cities S, A, B, C, D and E. The number beside each road gives its length. A postal worker starts at S and wants to visit four other cities. If the total distance travelled is as short as possible, which city will the postal worker not visit?
There are some sweets in a bowl. Sally takes half of them. Then Tom takes half of the sweets that remain. Next, Clara takes half of the remaining sweets. Finally, 6 sweets are left. How many sweets were in the bowl at the start?
Bunny’s mother has bought a white eraser and a pink eraser. They have the same width but different lengths. Bunny arranges them as shown. How many centimetres long is the pink eraser?
Five cards on a table are in the order 5, 1, 4, 3, 2. Alex wants to put them in the order 1, 2, 3, 4, 5. In one move, Alex may swap any pair of cards. What is the smallest number of moves needed?
The face of a clock is broken into four pieces. The sums of the numbers on the four pieces are four consecutive whole numbers. Which clock below has this property?
A ribbon has equally spaced holes, 2 cm apart, as shown. Its ends are joined to form a circle. How many centimetres greater is the circumference when the ends overlap at one hole than when they overlap at five holes?
Diagram labels: “Dải băng” means ribbon. The circular diagram shows the ribbon joined with one pair of holes overlapping.
