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Forwards Add Backwards printable worksheet
Can you find the other two ways of making $747$ in this way?
Which other numbers between $700$ and $800$ can be formed from a number plus its reversal?
There are more than five...
Can you explain how you know you have found all the possible numbers?
How many numbers between $300$ and $400$ can be formed from a number plus its reversal. And between $800$ and $900?$...
The number $1251$ can be formed by adding a $3$-digit number with its reversal.
Which other numbers between $1200$ and $1300$ can be formed from a number plus its reversal? And between $1900$ and $2000?$...
With thanks to Don Steward, whose ideas formed the basis 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?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.