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Reach 100

Age 7 to 14 Challenge Level:

Here is a grid of four "boxes":

Square divided into four.

You must choose four different digits from $1 - 9$ and put one in each box. For example:

Square divide into four, with 5,2,1 & 9 in the sections.

This gives four two-digit numbers:

$52$ (reading along the $1$st row)
$19$ (reading along the $2$nd row)
$51$ (reading down the left hand column)
$29$ (reading down the right hand column)

In this case their sum is $151$.


Try a few examples of your own.
Is there a quick way to tell if the total is going to be even or odd?


Your challenge is to find four different digits that give four two-digit numbers which add to a total of $100$.

How many ways can you find of doing it?
 



This problem is adapted from Make 200 from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES.