**C.1297. ****How many six-digit cube numbers are there?**

**C.1298.**** The sum of two whole numbers (both greater
than 10) is 1000. Prove that the last three digits of the squares of these two
numbers are identical?**

**C.1299.**** Stick another digit into the six-digit
number 975 312 (even in front or at the end) so that the new number would be
divisible by 468.**

**C.1300.**** How big could the greatest prime-divisor of
the ababab type 6-digit numbers in base 10 be?**

**C.1301.**** Find the greatest whole number which is not
the sum of 100 composite numbers.**

**C.1302.**** A computer responds to the following six
commands:**

**1) Let the
starting value of X be 3, and the starting value of S be 0.**

**2) Increase
the value of X by 2.**

**3) Increase the
value of S by X.**

**4) If S is
at least 10 000, then complete the 5th command, otherwise go back to the 2nd
command.**

**5) Print the
value of X.**

**6) Stop**

**What will
the computer print out?**

**C.1303.**** How many 10-digit numbers are there in
which only the digits 2 and 5 appear, and there are no digit 2s next to each
other?**

**C.1304. Is it possible to write the first six positive whole numbers on the perimeter of a circle so that for any three a, b, c consecutive numbers on the circle**

** is divisible by 7?**

**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