Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Coffee

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

Table Total

Age 14 to 16 Short Challenge Level:

Adding up all of the numbers and symbols in the table
Total =  + 4 + ( + 4) + 8 +  + ( + 8) + ( + 8) + ( + 4) + 16

= 3$\times$ + 3$\times$ + 52

Bottom row (or last column):
( + 8) + ( + 4) = 16, so  +  + 12 = 16, so  +  = 4

Then, multiplying by 3,
3$\times$ + 3$\times$ = 12

So Total = 12 + 52 = 64

Using the rules in the table to find the total
Reds add up to 16
Yellows add up to 16         Purples add up to yellows

Total = 16$\times$4 = 64

You can find more short problems, arranged by curriculum topic, in our short problems collection.