# Equations and Formulae Stage 4 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Equations and Formulae - Stage 4.

### Interstellar

##### KS 3 Short Challenge Level:

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

### Carry Over

##### KS 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

##### KS 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

##### KS 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.

### Months and Years

##### KS 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?

### Table Height

##### KS 3 Short Challenge Level:

Weekly Problem 21 - 2006
A table has blocks of wood placed on and next to it. Can you work out how tall it is?

##### KS 3 & 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

##### KS 3 & 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?

### Big Fish

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 21 - 2007
Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it. The tail weighed 9kg and the head weighed the same as the tail plus one third of the body. The body weighed as much as the head and tail together. How much did the whole fish weigh?

### I Love Musical Stars

##### KS 3 & 4 Short Challenge Level:

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

### Near 10

##### KS 3 & 4 Short Challenge Level:

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

### Algebraic Average

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 11 - 2008
The mean of three numbers, x, y and z is x. What is the mean of y and z?

### Leftovers

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

### Weighing the Baby

##### KS 3 & 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?

### Weighing Scales

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 35 - 2008
A child's box of bricks contains cubes, cones and spheres. Can you work out how many spheres will balance a single cone?

### Simultaneous Multiplying

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 17 - 2007
If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?