I've recently written a program which searches for all the numbers you can make from a set of inputs in this way (and is also adaptable to the slightly different rules of the Countdown numbers game). It thinks the possibilities given four 7s start off 1-10, 12-15, 18, 28; so if you got 23 or anything near it then either there's a bug in my program or you weren't playing by exactly the same rules...
It turns out that anyone playing my dad's version in 1872 would have had the most fun of anyone: you can get into the 80s before meeting an impossible number.
I also played a similar game involving four 4s, but that one seemed to have more open-ended rules: you were allowed to do any mathematical operation you could think up which didn't need a number to be written down to express it. So you could raise things to the power 4, you could write √4 any time you needed a 2, and I vaguely remember finding a use for ⌊cosh 4⌋ = 27.
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It turns out that anyone playing my dad's version in 1872 would have had the most fun of anyone: you can get into the 80s before meeting an impossible number.
I also played a similar game involving four 4s, but that one seemed to have more open-ended rules: you were allowed to do any mathematical operation you could think up which didn't need a number to be written down to express it. So you could raise things to the power 4, you could write √4 any time you needed a 2, and I vaguely remember finding a use for ⌊cosh 4⌋ = 27.