# Enigmatic Code

Programming Enigma Puzzles

## Puzzle #42: The card conundrum

From New Scientist #3265, 18th January 2020 [link]

Carl scribbled down an equation that contained only numbers and the letter X on a scrap of paper and left it on a table:

Bob found the card and realised that this was just a straightforward algebra problem. “I’ve found the solution”, he announced a minute later, dropping the card back on the table and leaving the room. Amy overheard him, walked over and picked up the card. After a while she announced: “That’s strange, I’ve found two solutions”.

Even stranger, Amy’s solutions were both different to Bob’s.

What were the solutions that Bob and Amy found?

[puzzle#42]

### 3 responses to “Puzzle #42: The card conundrum”

1. Jim Randell 21 January 2020 at 9:40 am

The expression on the card appears to be:

x / 6 = 1 – (1 – x) / 8

Which simplifies to:

x = 21

In this case both sides of the original expression evaluate to 7/2.

So this is the value that Bob found.

If Amy were to read the card upside down she would interpret it as:

8 / (x – 1) – 1 = 9 / x

This simplifies to:

x² = 9
x = ±3

In this case both sides of the original expression evaluate to ±3.

So these are the two values that Amy found.

2. Hugh Casement 21 January 2020 at 1:47 pm

If I = 1 then one would expect X to be 10. Or if X can take several values then why not I?
Very strange.

• Jim Randell 21 January 2020 at 2:09 pm

The I-like symbol is always interpreted as a 1, either way up. The only variable is X.

I think they chose a 1 that looks like a stick so that it sort of works either way up.

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