Or search by topic
This problem follows on from What Numbers Can We Make?
The interactivity below creates sets of bags similar to those in What Numbers Can We Make?
Investigate what numbers you can make when you choose three numbers from the bags. Once you think you know what is special about the numbers you can check your answer.
You can also find what is special when you choose four, five or six numbers.
When you have an efficient strategy, test it by choosing 99 or 100 numbers.
Always enter the biggest possible multiple. The "plus" number may include zero.
Can you explain your strategies?
If the bags contained 3s, 7s, 11s and 15s, can you describe a quick way to check whether it is possible to choose 30 numbers that will add up to 412?
There are a few related problems that you might like to try:
Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?