**B.1257. ****Two apricots and a pear are lighter than two
apples and a pear, but this second group is lighter than two pears and an
apricot. The same fruits have the same weight. Which fruit is the lightest?**

**B.1258.**** Find the smallest possible 2-digit number with the most
possible divisors.**

**B.1259.**** How many different ways can you pick two different
positive whole numbers, so that none of them is greater than 20 and their
product is divisible by 10?**

**B.1260.**** There are 3 discs rotating around the same axle in a toy.
There are 12 pictures of fruits on each disc, and every time the discs stop
spinning, only one picture can be seen on each disc through a small window for
each disc. One of the discs has 4 lemons, 4 bananas and 4 oranges; another disc
has 4 lemons, 4 oranges, and 4 bananas; and one has 2 lemons, 2 bananas, 2
oranges, 2 lemons, 2 bananas, and 2 oranges, in the order of the rotation of
the discs. (It means that if the discs rotate slowly, these are the orders of
the pictures appearing in each window.) When you pull the arm to rotate the
discs, they will rotate so fast that you cannot see the pictures on them until
they all stop at the same time. The rotation of the discs is set so that they
always stop 7 places ahead of the previously shown pictures. At the beginning
of the game each window showed a lemon on the disc behind that window. If you
pull the arm once to rotate the discs, then from left to right orange, lemon,
orange can be seen in the windows. If you pull the arm one more time, then
banana, banana, lemon can be seen in the windows from left to right. Which disc
is in which place in the toy?**

**B.1261.**** Write the following numbers as the sum of two square
numbers:**

**a) 10**

**b) 100**

**c) 1000**

**B.1262.**** We made a big cube out of small, unit cubes. We painted
every sides of the big cube blue, and then we took the big cube apart. There we
72 small cubes with exactly 2 sides painted blue. How many small cubes have
exactly 3 blue sides?**

**B.1263.**** In some countries the date at Christmas is written as
12/25, but in other countries they write it as 25/12. Life takes you to a
foreign country where you do not know which way they write the dates.**

**a) How many dates are there in a year about which you cannot
decide for sure which day they represent?**

**b) How many dates are there in a year that do not allow you to
know which way that country uses to write the dates?**

**B.1264. Peter has to vacuum the apartment. It takes twice as long to clean the living room than his own room, and he finishes the kitchen in 3 less minutes than the hallway. He cleans his own room for 5 minutes longer than the hallway, and he finishes the whole job in 37 minutes. How long does Peter vacuum in the living room and his own room together?**

**Please send your solutions here.**

The **Sharma Kamala Educational Trust** is sponsoring the participation of students from India. So, if you are **a student living in India**, please, send your solutions to: Group B from India