**B.1289. ****Fill in the blanks in the following diagram, so that in every row and
every column there would be exactly one 1, 2, 3, 4, and 5.**

**B.1290. We made the following 8 identical triangles using 16 toothpicks. Take away 4 toothpicks so that the number of remaining identical triangles is:**

**a) 6**

**b) 5**

**c) 4.**

**Every toothpick that
remains on the diagram must belong to at least one of the triangles, and each
remaining diagram must contain only triangles. **

**B.1291.**** For how many 3-digit numbers are at least one of the following 2
statements true?**

**– There is a digit 5 at
the hundreds place.**

**– There is a digit 3 at
the units place.**

**B.1292.**** There are only truth tellers and liars in a village. The truth tellers
always tell the truth, the liars always lie. Albert, Ben, Charlie and Dan live
in this village. One day they had the following conversation:**

**Albert: We are all liars.**

**Ben: You are the only liar
amongst us.**

**Charlie: You are both
liars.**

**Who are the liars and who
are the truth tellers in this group?**

**B.1293.**** There is a very strange analog clock in my room. It looks like a
regular 12-hour clock, but it takes 4 seconds (instead of a minute) for its
second hand to go around once. The other two hands follow the movement of the
second hand as they do on a regular clock. At exactly 9 am, my strange clock
shows 4 hr 20 min 0 seconds. What time does my strange clock show at 9:50 am on
the same day? **

**B.1294.**** Find the greatest and the smallest positive whole number in which the
product of the digits is 120.**

**B.1295.**** Find all those 3-digit numbers in which both: the number created from
the first two digits, and the number created from the last two digits, are
square numbers. **

**B.1296. Kate added six positive whole numbers, and the sum turned out to be 2019. Then she multiplied the same six numbers, and realized that the last digit of the product is 3. She is sure about her additions. Could her multiplications be all correct, also?**

**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