Ruler Puzzle

[Eoin Monaghan]

A ruler company called StraightLine has been making rulers which are 13cm long. But the company is poor and can only afford to put enough ink on for FOUR digits. The manager is smart and realises he can use 4 numbers but still be able to measure 1cm to 13cm. What 4 measurements does he make?

Example. The numbers 1cm, 4cm, 8cm and 13cm.
You could make 1cm because it is there, 2cm you can't, 3cm by going from 1cm to 4cm, 4cm is there, 5cm by going from 8cm to 13cm and so on and so forth. I got this as a puzzle in school once.

[Eoin Monaghan]

Kieran has PMed me a correct answer (different to mine, but still valid).

[Gavin Chipper]

1, 4, 5, 11

1=1
13-11=2 (measuring backwards from the end)
4-1=3
4=4
5=5
11-5=6
11-4=7
13-5=8
13-4=9
11-1=10
11=11
13=1=12
Whole ruler=13

[Kirk Bevins]

But the company is poor and can only afford to put enough ink on for FOUR measurements.

Would be fine if you said 4 digits, but 4 measurements? Surely the company can afford maybe 6 or 7 digits? Nice puzzle but a bit contrived.

[Eoin Monaghan]

Gavin is correct, again with a different answer to mine.

[Matt Morrison]

Gavin wins. Kieran's just fucking spooky these days, reading the forum without signing in, bad jokes in aptochat, PMing puzzle answers when everyone else is taking part in the thread. The new Bolas.

[Michael Wallace]

Nice puzzle but a bit contrived.

How were you ever a maths teacher?

[Eoin Monaghan]

Howard has it right with another different answer, clearly more than one method of solving.

Additional puzzle: How many different methods can you find?

[Jimmy Gough]

Kieran's just fucking spooky

Yep.

[Howard Somerset]

Additional puzzle: How many different methods can you find?

I've found three essentially different ways

but that's actually six if you include reflections.

1, 2, 6, 10
1, 4, 5, 11
1, 6, 9, 11
and their reflections
2, 8, 9, 12
2, 4, 7, 12
3, 7, 11, 12

[Ian Volante]

Additional puzzle: How many different methods can you find?

I've found three essentially different ways

but that's actually six if you include reflections.

1, 2, 6, 10
1, 4, 5, 11
1, 6, 9, 11
and their reflections
2, 8, 9, 12
2, 4, 7, 12
3, 7, 11, 12

They all have more than four digits!

[Howard Somerset]

They all have more than four digits!

lol

As has the original example in the question Eoin posed. I think the original post should have said NUMBERS rather than DIGITS.