Posing Questions and Making Conjectures - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Posing Questions and Making Conjectures.

Ones, Twos and Threes

Age 11 to 14 Short Challenge Level:

Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

Leaning Over

Age 11 to 14 Short Challenge Level:

Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

Eulerian

Age 14 to 16 Short Challenge Level:

Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Little Difference

Age 14 to 16 Short Challenge Level:

What is the value of $2015 \times 2017 - 2016 \times 2016$?

Last-but-one

Age 14 to 16 Short Challenge Level:

What is the last-but-one digit of 99! ?

Super Computer

Age 14 to 16 Short Challenge Level:

What is the units digit of the given expression?

Producing an Integer

Age 14 to 16 Short Challenge Level:

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?