A maths problem

[Sharad M.]

Divide $534 (in whole $ increments) into a number of bags so that I can ask for any amount between $1 and $534, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will require? And how much in each bag?

[Jon Holdman]

Sorry, that's trivial. Use binary numbers. You need 10 bags. The first nine hold $1, $2, $4, $8, $16, $32, $64, $128, $256. That's $511 total, so the last bag holds the remaining $23. For any requested amount less than $511, just hand over the proper combination of the first nine bags. For amounts from $512 to $534, hand over the $23 bag, subtract $23 from the requested amount and then apply the first half of the solution.

This is actually a useful problem for real estate. If you go to the trustee sale and they require a cashier's check for the bid amount, but you don't know where the bidding will end, just bring checks arranged like this and hand over the proper set of checks.