One to Nine Equals a Hundred Quiz Puzzle - Answer

We asked a trickier puzzle on Friday than the previous week; back to the normal degree of difficulty, although it’s another deceptively simple puzzle.

Take the digits one through to nine in order and, without changing their order, insert three mathematical symbols to make a sum. The result of this sum must equal 100 exactly. You can use the same symbol more than once, but each time you use the symbol that counts towards the total of three. That is, two multiplies and a subtraction is three symbols.

For example, you could have

1 x 2345 – 678 + 9 = 1676

But that does not equal 100!

The answer is 123 – 45 – 67 + 89 = 100

A good way to approach this is to realise that the final digits of the four parts (there must be four parts because of the three symbols) must add up to zero or a multiple of ten. This means the four parts must all be odd or all even, and as the final part (ending in 9) is odd, they must all be odd. So 3, 5, 7 and 9 can be arranged 3 – 5 – 7 + 9 to equal zero, and this happens to give the correct answer when expanded to the full equation.


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