Highest amount (trickey one)

[cruzloco]

If you only have 5p stamps and 13p stamps what is the highest amount?

[brachiopod]

Is there something missing from your question?

The highest value postage you could pay is 5x + 13y, where x is the number of 5p stamps you have and y the number of 13p stamps - (you do say "stamps" plural in your question.)

Apart from that, your question lacks sufficient information to make any further sense.

[cruzloco]

True sorry about that question is: If you only have 5p stamps and 13p stamps what is the highest amount, you are unable to pay by just using stamps?

[dzug]

Try the quizzes and puzzles section.

A 'trickey' answer would be that you can't pay in stamps at all - they are neither legal tender nor an accepted form of currency.

[cruzloco]

come to think of it, must be a straight forward answer as they suppose to be straight forward questions

[dasherman]

I'm assuming you're talking about sending mail,if so it depends how heavy your package is and so how much the postage is.

[cruzloco]

its not a matter of thinking what it could be its a matter of thinking whats the highest amount. Question finishes by saying "you are unable to pay just by using stamps"

[rja211077]

you're right, a devilishly tricky one, but i make the answer 66. do i win a prize?

[rja211077]

by the way, i am guessing that the question should be worded as follows: 'if you have an unlimited number of both 5p and 13p stamps, what is the highest amount you are unable to pay exactly?'.

[rja211077]

or to put it mathematically: 5x+y "does not equal" z. For the case where x and y are positive integers or zero, what is the highest value of z?

[rja211077]

sorry, made a mistake, 66 is 8x5+2x13. i now think it's 47p

[cy marven]

I think there is no limit, i guess you are however restricted by the size of the package as there will only be so much room. In theory if your parcel cost �5 to send you could put 500 penny stamps on it, it would however need to be a very big parcel to fit them all on.
Cy Marven

[cruzloco]

remember you are unable to pay by just using stamps

[rja211077]

the question's intended wording is clearly "what is the highest amount you are unable to pay by just using stamps". so in other words, you are only allowed to use stamps. the answer is 47p, as i stated.

the way you have put a comma in after "amount" confuses the matter and in fact makes the question nonsensical.

[cruzloco]

what formular did you use to get to answer 47p?

[samuel23]

Sorry I don't get it. If you only have 5p and 13p stamps how would you get the amount 19p, 21p, or 22p? Also if you had an unlimited amount of stamps surely the question (the accuracy of which seems to be in dispute here) is what is the highest amount you are unable to pay just by using the AVAILABLE stamps (possibly with the added requirement of or you must use both amounts) the answer will still be 19p. I would like to bet that there is another stamp of a different value that has not been included in this question, or the equation would be too simple. eg 5 x 3 = 15 ~or~ 5 + 13 = 18 ~or~ 5 x 4 = 20. thus 19p being the first amount not able to be made by using both values

[rja211077]

it's not a problem that can be solved with a simple formula. the best way of solving the problem is to work through it like this:

the numbers you are able to make are represented by the formula 5x+13y where x is the number of 5p stamps you use, y is the number of 13p stamps.

numbers ending in 0 (10, 20, 30, etc) can all be made easily when x is even and y is zero, so the answer doesn't end in zero

numbers ending in 1 can be made where y=2 (or 12, 22, etc) and x is odd. The lowest is 5*1+13*2 = 31, therefore the highest number that cannot be made this way is 21.

numbers ending in 2 can be made where y = 4 (or 14, 24, etc) and x is even. The lowest is 5*0+13*4 = 42, therefore the highest number that cannot be made this way is 32.

numbers ending in 3 can be made where y is 1 and x is even, the lowest is 5*0+13*1 = 13, therefore the highest that cannot be made is 3.

numbers ending in 4 can be made where y is 3 and x is odd, the lowest is 5*1+13*3 = 44, therefore the highest that cannot be made is 34.

numbers ending in 5 are made where y is 0 and x is odd. obviously every number ending in 5 can be made this way.

numbers ending in 6 are made where y is 2 and x is odd, the lowest is 2*13 + 5*0 = 26, therefore the highest that cannot be made this way is 16

numbers ending in 7 are made where y is 4 and x is odd, the lowest is 4*13 + 5*1 = 57, therefore the highest that cannot be made this way is 47.

numbers ending in 8 are made where y is 1 and x is odd, the lowest is 1*13 + 1*5 = 18, therefore the highest that cannot be made this way is 8.

numbers ending in 9 are made where y is 3 and x is even. the lowest is 13*3 + 5*0 = 39, therefore the highest that cannot be made is 29.

so you are left with the answer that the highest number that cannot be made is 47.

[samuel23]

ok rja ~ I get that now. But surely 47 isnt the highest number. There has to be some sort of limit or you could say 3254 or 6504 .

[rja211077]

any number above 47 can be made using the logic above. to use your examples, 3254 can be made by 13*3+654*5 (or 13*13+617*5, or 23*13+591*5, etc etc), similarly 6504.

the question is, what's the HIGHEST number that CAN'T be made (exactly).

answer: 47

[jessiedog]

Surely the answer is 12p.

No multiplication of 5p equals 12p and 13p is too much straight away.

[brachiopod]

True, jessie, but the question, as rja emphasised in the post just before yours:

What is the HIGHEST amount that CAN'T be made exactly with only 5p and 13p stamps?

So, given ONLY 5p and 13p stamps, you obviously can't make 1p, 2p, 3p, 4p, 6p, 7p, 8p, 9p, 11p,12p, 14p, 16p and 17p - but these are the LOWEST amounts.

Meanwhile, you could make �1,000,000.01p with 19,999,995 x 5p stamps and two 13p stamps.

So the given answer of 47p is the HIGHEST amount that CANNOT be made with 5p and 13p stamps.

Everything above this value is possible;

eg
48p = 1 x 13p and 7 x 5p
49p = 3 x 13p and 2 x 5p
50p = 10 x 5p (obviously)
51p = 2 x 13p and 5 x 5p etc. etc