Snack time

[Jezza]

A few months ago Mr and Mrs Jezza Bear went out for the day to the city. Whilst doing the shopping they
decided to stop at a pleasant cafe in the heart of the old town. They decided to have a nice cool drink each
and some tasty pastry snacks. The waiter tells them that the pastry snacks are only served in portions of
6, 9 or 20.


The question: What is the biggest number of pastry snacks that cannot be ordered in these portions?

[HansV]

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">37</span hide>

[mbarron]

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">43</span hide>

[HansV]

Oops, you're correct! <img src=/S/thumbup.gif border=0 alt=thumbup width=15 height=15>

[HansV]

Sadly, Jezza seems to have forgotten to award you a [choccy bar]...

[Jezza]

Sorry for the delay in answering, I have not been active in the Lounge this weekend. It appears Hans has provided you with a [choccy bar] already( <img src=/S/whisper.gif border=0 alt=whisper width=29 height=17>Probably one of the many he has won in recent times <img src=/S/grin.gif border=0 alt=grin width=15 height=15>) so to make up for it you can also have a [tasty pastry snack].

[rk_winston]

Could you please provide the solution? The way I see it, it is a trick question or, I was up too late watching the Super Bowl commercials and just too tired to think this morning.

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">I can order for any amount I want and take any remainders home in a doggy bag. For 37 pastries, I order two orders of 20 and take home three and for the 43 pastries, I order the 20 and 6 size orders and take home three.</span hide>

[Jezza]

Certainly sir

I have attached it in a text document for you to peruse at you leisure <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

[HansV]

You're correct, of course, but the idea of the puzzle is to stick to numbers you can order exactly by order multiples of 6, 9 and 20 items. Putting some items in a doggy bag is not playing by the rules.

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Combining mutliples of 6 and 9, you can order any multiple of 3 starting at 6: 6, 9, 12, 15, ...
Adding 20, you can order any (multiple of 3 plus 2) starting at 26: 26, 29, 32, 35, ...
Adding another 20, you can order any (multiple of 3 plus 1) starting at 46: 46, 49, 52, 55, ...
The only numbers not available are 1, 2 ,3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, and 43.</span hide>