Tuesday 31 January 2017
Problem 31
A two-digit integer n has the property that the sum of n and its digits is equal to 63. Find n.
Monday 30 January 2017
Sunday 29 January 2017
Saturday 28 January 2017
Problem 28
Let ABC an isoceles triangle with AB = AC = x, BC = y. Let denote M the midpoint of AB. Find the length of CM.
Friday 27 January 2017
Thursday 26 January 2017
Problem 26
Prove that every composite number has a proper factor less than or equal to its square root.
Wednesday 25 January 2017
Tuesday 24 January 2017
Problem 24
In a hall, there are 1098 seats. There are two aisles. Each row has the same number of seats. In each row, the number of seats between the aisles is 31. The rest of the seats are equally divided between the aisles. Find the number of rows.
Monday 23 January 2017
Problem 23
If f: R→ R (where R is the set of all real numbers) is given by f(f(x)) = 4x + 6. Find f(x).
Sunday 22 January 2017
Saturday 21 January 2017
Problem 21
Prove that the a composite n non divisible by is a semiprime.
Friday 20 January 2017
Problem 20
Find the last digit of 4343.
Thursday 19 January 2017
Wednesday 18 January 2017
Problem 18
Given a Pythagorean triple a, b, c, prove that if a is odd, then either b or c must be odd.
Tuesday 17 January 2017
Monday 16 January 2017
Sunday 15 January 2017
Problem 15
Prove that if n is an odd number, then n, 0.5
(n2 - 1) and 0.5 (n2
+ 1) form a Pythagorean triple.
Saturday 14 January 2017
Friday 13 January 2017
Thursday 12 January 2017
Wednesday 11 January 2017
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