I made up a math card game today that was pretty clever (if I do say so myself! 🙂 ) with the intention of playing it with Leo, but it turned out to be so hard that even I couldn’t play it!

First remove the face cards and jokers from a standard deck, leaving only the numbers (and ace = 1). Shuffle, and deal four cards to each player.

Unlike most games, this one is *collaborative* — the players work together to reach the goal. That goal being for both players to make the *same* final number from each of the set of four random numbers that you’ve been dealt, using standard arithmetic operations (and including forming a number out of separate digits, for example, making 1 and 2 into 12 or 21).

Here’s an example hand:

Player A: 7, 8, 5, 10

Player B: 2, 10, 2, 3

And here are some results that can be obtained:

43: 10-(7-(5*8)) and 3+(2*(2*10))

64: 8*(10+(5-7)) and 2*(2+(3*10))

1: 10/(8-(5-7)) and 2/(10/(3+2))

(Actually, the game is much easier if you can make a zero, like Player B can above, as 2-2, because that lets you drop out as many values a you like through multiplication by zero. Probably trivial operations like multiplication by zero, shouldn’t be allowed.)

Unfortunately, the game is way too hard. Leo was actually pretty good at doing the calculations, but the search problem of finding the same number among the tens of thousands of possible combinations of arithmetic operations is just way too hard. In fact, I ended up writing a program to solve the problems exemplified above!

There are some easy cases, like the zero I mentioned above, that enable you to simplify, but in playing about five hands, we managed to not get even a single one…even when I was doing all the work of searching for a solution.

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Robyn

said:You may know of this book already but if you love hard puzzles (well, hard for me) , you will like Moscow puzzles!! Edited by the famous Martin Gardner

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