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?
Trinni is fascinated by triangle numbers (1, 3, 6, 10, 15, 21, etc.) and recently coming across a clock, she found that she could rearrange the twelve numbers 1, 2, 3, ..., 12 around the face so that each adjacent pair added up to a triangle number. She left the 12 in its usual place; what number did she put where the 6 would usually be?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.