# Equations and Formulae Stage 4 - Short Problems

### Interstellar

##### Stage: 3 Short Challenge Level:

Weekly Problem 22 - 2012
What number could replace * so that */5 is between 3 and 4?

### Weekly Problem 1 - 2008

##### Stage: 3 and 4 Challenge Level:

Given that the number 2008 is the correct answer to a sum, can you find n?

### Weekly Problem 11 - 2008

##### Stage: 3 and 4 Challenge Level:

The mean of three numbers, x, y and z is x. What is the mean of y and z?

### Weekly Problem 26 - 2008

##### Stage: 3 and 4 Challenge Level:

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

### Weekly Problem 35 - 2008

##### Stage: 3 Challenge Level:

A child's box of bricks contains cubes, cones and spheres. Can you work out how many spheres will balance a single cone?

### Carry Over

##### Stage: 3 Short Challenge Level:

Weekly Problem 24 - 2009
Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

### Unequal Statements

##### Stage: 3 Short Challenge Level:

Weekly Problem 32 - 2010
For what numbers are each of these statements true? How many of the statements can be true at the same time?

### Named Products

##### Stage: 3 Short Challenge Level:

Weekly Problem 42 - 2010
Can you find the solution to this equation? Each of the different letters stands for a different number.

### Near 10

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 4 - 2011
10 must remain within easy reach...

### Months and Years

##### Stage: 3 Short Challenge Level:

Weekly Problem 1 - 2013
The product of Mary's age at her last birthday and her age in complete months is 1800. How old is Mary?

### Weighing the Baby

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 2 - 2014
Weighing the baby at the clinic was a problem. Can you work out the total weight of the baby, the nurse and me from the information given?

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 3 - 2015
In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

### In the Hundreds

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 21 - 2015
For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?

### I Love Musical Stars

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 42 - 2015
Each row and column has the total given. What is the value of the heart symbol?

### Squeezed In

##### Stage: 3 Short Challenge Level:

Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?

### Standing on the Table

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 39 - 2017
Clement and Dmitri both measure how much taller they are standing on a table compared to the other standing on the floor. Can you work out how tall the table is?

### Sharing Sweets

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 41 - 2017
Maria and Lucy spun a coin 30 times, and gave each other sweets depending on the outcome of the spin. How many times was tails spun?