**B.1249. ****What is the last digit of the following
product:**

**2015 x 2017 x 2019 x 2021**

**B.1250.**** The first three elements of a number sequence are 3, 1, 1.
Starting with the second element, the product of the two neighbors of any
element is the same. What is the sum of its first 2019 elements?**

**B.1251.**** Using the positive whole numbers, we created the following
series of fractions. What number goes in place of the question mark?**

**1/1, 2/2, 3/1, 4/3, 5/2, 6/1, 7/4, 8/3, 9/2, 10/1, …, 2019/?**

**B.1252.**** Mr. Shee Lee Hoi is the owner of the most famous
restaurant in Hong Kong. Once he decided that he will write his name on the
window by using straight neon line-segments, so that you could figure out the
phone number of his restaurant by looking at the sign. What is that 10-digit
phone number?**

**B.1253.**** To a whole number add the number you get by reversing the
digits of the original number. Can the sum be 2019?**

**B.1254.**** How many rectangles with whole number long sides have
perimeter equal to 2019?**

**B.1255.**** How many rectangles with whole number long sides have area
equal to 2019?**

**B.1256.**** 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. The first disc has 4 lemons, 4 bananas and 4 oranges; the second
disc has 2 lemons, 2 bananas, 2 oranges, 2 lemons, 2 bananas, and 2 oranges;
the third disc has a lemon, a banana, an orange, a lemon, a banana, an orange,
and so on, 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 the
first lemon of an all-lemon segment on the disc behind that window.**

**a) How many times do we have to pull the arm in order to see 3
oranges for the first time?**

**b) Can we ever see 3 bananas?**

**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