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

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

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.

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.

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.

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