Here is a problem from the UKMT Senior (17-18 year-old) Mathematics Challenge for 2009:
“Four positive integers a, b, c, and d are such that
_________abcd + abc + bcd + cda + dab + ab + bc + cd + da + ac + bd + a + b + c + d = 2009.
What is the value of a + b + c + d?
_________A 73_________B 75_________C 77_________D 79_________E 81”
See the Challenging Sum
(Update 4/17/2019) Continue reading
This is another UKMT Senior Challenge problem, this time from 2006.
“A toy pool table is 6 feet long and 3 feet wide. It has pockets at each of the four corners P, Q, R, and S. When a ball hits a side of the table, it bounces off the side at the same angle as it hit that side. A ball, initially 1 foot to the left of pocket P, is hit from the side SP towards the side PQ as shown. How many feet from P does the ball hit side PQ if it lands in pocket S after two bounces?”
Pool Partiers should have no difficulty solving this. See More Pool.
This is a fun little problem from the United Kingdom Mathematics Trust (UKMT) Senior Math Challenge of 2008.
“What is the remainder when the 2008-digit number 222 … 22 is divided by 9?”
(Hint: See The Barrel of Beer) See A Multitude of 2s.
This is an interesting problem from the United Kingdom Mathematics Trust (UKMT) Senior Math Challenge of 2008.
“The length of the hypotenuse of a particular right-angled triangle is given by √(1 + 3 + 5 + … + 23 + 25). The lengths of the other two sides are given by √(1 + 3 + 5 + … + (x – 2) + x) and √ (1 + 3 + 5 + … + (y – 2) + y) where x and y are positive integers. What is the value of x + y?”
See the Right Triangle with Roots.