Rakesh's number puzzle

Rakesh gives you a challenge. 'I have thought of two numbers. Their sum is 25, and their difference is 11. Can you tell me the two numbers?'

You do not need any formula. Try different pairs and check two things each time: do they add up to 25, and is the difference between them 11? Remember that DIFFERENCE means first number minus second number, so the order matters.

Keep a table. Try 10 and 15: sum 25, difference −5. Try 20 and 5: sum 25, difference 15. Try 19 and 6: sum 25, difference 13. Each guess keeps the sum right and walks the difference closer.

Try 18 and 7: sum 25, difference 11. That is the pair.

Now Rakesh's second challenge: two numbers whose sum is 25, but whose difference is −11. Use the same method and fill the table again.

You will notice something quicker than searching. Swap the numbers from the first puzzle and the sum stays 25 while the difference changes sign. So the answer is first number 7, second number 18.

Try more pairs: sum 27 with difference 9; sum 4 with difference 12; sum 0 with difference 10; sum 0 with difference −10; sum −7 with difference −1; sum −7 with difference −13. Then play it with a partner — one thinks of two integers and gives their sum and difference, and the other works them out.