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# Two and Two

**How many solutions can you find to this cryptarithm?**

How can you be sure you have found them all?

**Can you create other similar cryptarithms?**

Here are some suggestions to start you off.

** ONE + ONE = TWO**

ONE + TWO = THREE

ONE + THREE = FOUR

FOUR + FIVE = NINE

**Can you make a cryptarithm subtraction?**
*If you enjoyed this problem you may like to take a look at Cryptarithms*
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*Two and Two printable worksheet*

Each of the different letters below stands for a different number.

How can you be sure you have found them all?

Here are some suggestions to start you off.

ONE + TWO = THREE

ONE + THREE = FOUR

FOUR + FIVE = NINE

Click here for a poster of this problem.

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.