In the 1960s another kind of number puzzles have become very popular. It's surprising how many numbers could be represented this way. For example, I can represent 100 with five threes as 100 = 33×3 + 3/3. One way is to attempt representing numbers with limited means. There are many ways to merrily spend time solving arithmetic problems. Here, for example, a representation of one that uses all ten digits: Variations include setting targets other than 100. This leads to a completely new set of problems with numbers having fractional parts. You may allow for operations other than addition and subtraction. To figure out why, it may be helpful to recollect the notion of digital roots. In fact, it is impossible to avoid subtraction even if the digits come in an arbitrary order.

And this is also true for all additive (the ones in which the only allowed operations are addition and subtraction) examples below. There is a keen observation that in the two examples above at least one of the operations is subtraction.

There appear to be more than just two answers. I do not claim to have made an exhaustive search but Signs between them so that the result of thus described arithmetic operation will be 100.Īnd suggested there existed at least one more. Start with the sequence of non-zero digits 123456789.

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