A Strange Calculator
I have a strange calculator. The four elementary calculations are not available, but there is a button (called OMG) which has the following property: if you enter the number press OMG, and enter the number then the result shown on the screen is . The change signs button and the calculator's memory are functioning normally, as are all the numbers from 0 to 9.
Is it possible to calculate the expression using the calculator only?
EDIT: You MUST only use the calculator to calculate the expression! (i.e. you must perform the calculation , then subtract the answer by , etc., using only buttons on the calculator). You CANNOT simplify the expression beforehand!
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The qualifier that you can’t simplify the expression is rather contrived, but it is nonetheless possible to work around.
First the addition and subtraction. These steps are actually quite easy, since any calculator with the memory function has to have, at the very least, a m+ button.
The multiplication is slightly harder. By doing (a OMG b) OMG 1, we get 1 − 1 1 − b a , which simplifies as b a . Making use of this, and the fact that a c b ⇒ c a b , we can perform the calculation. The keypresses, in order, are
2018 M+ 2019 M+ -2020 M+
2022 OMG MR MC
ANS OMG 1 Enter M+
2021 OMG MR MC
ANS OMG 1
I’ve used M+ for memory add, MR for recall, MC for memory clear, ANS for last amswer recall, and Enter for hitting enter. There should probably be other enter presses in certain steps to make sure the calculation goes correctly, but I felt this one was important for clarity. Also, if the calculator doesn’t have an ANS function, add M+ to the end of the last line, then replace ANS with MR MC.