**C.1281. ****Sara, Kate, and Sophie want to buy the same book. However, none of them have enough money to buy
it. Sara is missing 1/3 of the price of the book, Kate is missing 1/4 of the
price of the book, and Sophie is missing 1/5 of the price of the book. If the
book were $4.70 cheaper then they could buy 3 copies of the book if they spent
all their money together. How much does
a copy of this book cost?**

**C.1282.**** Every competitor in a building competition has to build a
continuous structure using 8 identical cubes so that each cube in the structure
shares at least one full side with each of its vertical and/or horizontal
neighbor. There can be no hole in the structure, cubes cannot be glued
together, and you have to be able to climb up from the floor level to the top
of the building one level at a time for each step. The value of a building is
the product of two numbers: the area of its base and its height. At the end of
the competition the judges were surprised to see that buildings by different
competitors received different scores. How many competitors could there be at
most in this competition? What was the value of the winning structure?**

**C.1283.**** There are 7 houses on Dragon Street, numbered from 1 to
7. Mailman, Deli Were, brought mail to exactly two of these houses each day
last week. Two of these houses never received mail; all the others received
mail twice last week. The sums of the house numbers where Deli went each day are:
Monday 5, Tuesday 8, Wednesday 9, Thursday 13 and Friday 7. (There is no mail
service on Saturdays and Sundays.) Which two houses did not receive mail?**

**C.1284.**** One year January 1 ^{st} fell on a weekday, while
December 31^{st} fell on the weekend (Saturday or Sunday). The school
year started on September 1^{st}. What day of the week was that?**

**C.1285.**** There are 3 kinds of chocolates, a total of 16 pieces in
a box, as shown on the diagram. The total mass of the 4 chocolates in the top
row is 14 dkg, and it is 11 dkg in the
row below that. The total mass of the 4 chocolates in the left column is 10
dkg. How many dkg of chocolate is there in the box?**

**C.1286.**** Place all the whole numbers from 1 to 9 in the circles of the house on the following
diagram so that the sum of the three numbers in any 3 circles falling on a
straight line is 13. How many different solutions are there? (Two solutions are
different if there is at least one circle with different numbers in it.)**

**C.1287. If you take the 2020 digit number with every digit equal to 2 and divide this 2020 digit number by 3, how many of the digits in the quotient will be a 7? **

**C.1288. In triangle ABC, angle B is the smallest, which is 1/5 of the sum of the two other angles. C is 4 cm from line AB. How long is side BC?**

**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 C from India