The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This was a very popular problem - we received
over 200 correct solutions including many from Oxgangs Primary
School in Edinburgh, Red Hill Field Primary School, Culford Prep
School, Jebel Ali Primary School in Dubai, Greenfields Junior
School, Howell's School in Cardiff,Archbishop Temple High School,
Stewart County Middle School, Hassall Grove P.S. in Australia,
St.Paul's Catholic College, Cardiff High School,Casterton
Preparatory School, Outwoods Edge Primary School, Thomas Deacon
Danielle from Howell's School in Cardiff
explained the strategy for getting the four friends across in the
Josh captured the different stages here
Patrick from Woodbridge School wrote:
Rhea and Macy from Mason Middle School found
another set of timings when both Strategies would give identical
Harry from Dumpton School compared the times
involved in each strategy:
Someone calling themselves "a very old person"
used the same reasoning to explain how to choose between the
Here are examples of each case:
2B = A+C (use either Strategy) when the times
are 4, 5, 6, and 7
A+C is greater than 2B (use Strategy 1) when
the times are 1, 2, 7 and 10 (as in the original problem)
A+C is less than 2B (use Strategy 2) when the
times are 1, 8, 9 and 10