# 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?

### Last-but-one

##### Age 14 to 16 Short Challenge Level:

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

### Little Difference

##### Age 14 to 16 Short Challenge Level:

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

### 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?

### Super Computer

##### Age 14 to 16 Short Challenge Level:

What is the units digit of the given expression?