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sum: 1abcde multiplied by 3 equals abcde1.



sum: 2fghij multiplied by 3 equals fghij2


Can you replace the letters with numbers?
Is there only one solution in each case?

Once you've had a chance to think about it, click below to see how two different pupils began working on the task.
 

Here is Abdullah's work:

"For each problem I first looked to find a number that would make the ones column accurate, then I substituted the number for the answer in the tens column and then continued the process until the calculation was complete."


Joshua wrote:

"I wrote out single digit multiples of three up to 9 because each letter was one digit. I noticed that the numbers 1 to 9 only appeared once in the ones column of the answers. I looked at the question and realised that 3 x e had to be 21 because it was the only answer ending in 1. This meant that e had to be 7.

I carried the 2 and took it from 7 (the other e) and got 5. So d x 3 had to end in 5 which meant d had to be 5 because 5 x 3 = 15. I then repeated the process."


Can you take each of these starting ideas and develop it into a solution?

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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