Exploring and Noticing - Short Problems

56 406 is the product of two consecutive numbers. What are these two numbers?

A pattern repeats every six symbols. What are the 100th and 101st symbols?

How many arm-wrestles will there be in the royal arm wrestling championship?

An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?

One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?

Weekly Problem 51 - 2016
Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

A sequence is generated using these rules. For which values of n is the nth term equal to n?

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

Jasmine buys three different types of plant. How many triffids did she buy?

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

Find the location of the point of inflection of this cubic.