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Think of Two Numbers

Age 11 to 14 Challenge Level:

Here is an alternative and more unusual version of the "Think of a Number" trick which you may have heard of before.

numbers 0-9

Think of two whole numbers under $10$.

Take one of them and add $1$.
Multiply by $5$.
Add $1$ again.
Double your answer.
Subtract $1$.

Add your second number.
Add $2$.
Double again.
Subtract $8$.
Halve this number and tell me your answer.

 

From your answer I can work out both your numbers very quickly. How?

Choose some different pairs of numbers and repeat the process.
Can you figure out how the trick works?
 

Click here for a poster of this problem.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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