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Double Digit

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?

What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Alphabet Soup

Age 11 to 14 Challenge Level:

This challenge is to make up YOUR OWN word-arithmetic challenge.

Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

The hard part is to make up some message rather than just using any old letters. Send in your word-arithmetic challenge, together with at least one solution to it.

Another challenge is to discover if the puzzle has just one solution or many. Here are two easy examples; they are just addition sums and you may be more inventive and make up subtractions, multiplications or divisions:
 

  N R I C H
+ S T A R S
  M A T H S
 
  M A T H
+ E M A T
  I C A L

Lastly, can you prove that

  N R I C H
+ M A T H S
  S T A R S

cannot be made to work?