This interesting problem comes from Colin Hughes at the Maths Challenge website.
“Problem
Prove that for any number that is not a multiple of seven, then its cube will be one more or one less than a multiple of 7.”
See Lucky 7 Problem
Tag Archives: algebra
Cube Roots Problem
In a June Chalkdust book review of Daniel Griller’s second book, Problem solving in GCSE mathematics, Matthew Scroggs presented the following problem #65 from the book (without a solution):
“Solve _______________
”
Scroggs’s initial reaction to the problem was “it took me a while to realise that I even knew how to solve it.”
Mind you, according to Wikipedia, “GCSEs [General Certificate of Secondary Education] were introduced in 1988 [in the UK] to establish a national qualification for those who decided to leave school at 16, without pursuing further academic study towards qualifications such as A-Levels or university degrees.” My personal feeling is that any student who could solve this problem should be encouraged to continue their education with a possible major in a STEM field.
See Cube Roots Problem for a solution.
A Tricky Product
This is a tricky product problem from Alfred Posamentier which naturally has a slick solution—if you can think of it.
“Find the numerical value of the following expression:
“_
See A Tricky Product for a solution.
Radical Radicals
This is another UKMT Senior Challenge problem, but for the year 2005. I thought it was diabolical and hadn’t a clue how to solve it. Even after reading the solution, I don’t think I could have come up with it. I take my hat off to anyone who solves it.
“Which of the following is equal to
See Radical Radicals for a solution.
Challenging Sum
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 for a solution.
(Update 4/17/2019) Continue reading