Math optimization riddle
$begingroup$
You have been given the task of transporting 3,000 apples 1,000 miles
from Appleland to Bananaville. Your truck can carry 1,000 apples at a
time. Every time you travel a mile towards Bananaville you must pay a
tax of 1 apple but you pay nothing when going in the other direction
(towards Appleland). What is highest number of apples you can get to
Bananaville
The answer is $boxed{833}$. However, I don't understand how to obtain this answer. Also, is there any way to show that the answer is optimal?
I have seen a riddle similar to this before, and I think the trick is to move $1000$ apples towards a stopping point, come back, get more to that stopping point, and so on. I can't figure this one out, though.
optimization puzzle
$endgroup$
add a comment |
$begingroup$
You have been given the task of transporting 3,000 apples 1,000 miles
from Appleland to Bananaville. Your truck can carry 1,000 apples at a
time. Every time you travel a mile towards Bananaville you must pay a
tax of 1 apple but you pay nothing when going in the other direction
(towards Appleland). What is highest number of apples you can get to
Bananaville
The answer is $boxed{833}$. However, I don't understand how to obtain this answer. Also, is there any way to show that the answer is optimal?
I have seen a riddle similar to this before, and I think the trick is to move $1000$ apples towards a stopping point, come back, get more to that stopping point, and so on. I can't figure this one out, though.
optimization puzzle
$endgroup$
$begingroup$
Doing a quick Google search will get you a method for $833$. See for example goodriddlesnow.com/riddles/hard/page:5/sort:Riddle.difficulty/… . This doesn't prove optimality though
$endgroup$
– pwerth
Jan 17 at 20:22
add a comment |
$begingroup$
You have been given the task of transporting 3,000 apples 1,000 miles
from Appleland to Bananaville. Your truck can carry 1,000 apples at a
time. Every time you travel a mile towards Bananaville you must pay a
tax of 1 apple but you pay nothing when going in the other direction
(towards Appleland). What is highest number of apples you can get to
Bananaville
The answer is $boxed{833}$. However, I don't understand how to obtain this answer. Also, is there any way to show that the answer is optimal?
I have seen a riddle similar to this before, and I think the trick is to move $1000$ apples towards a stopping point, come back, get more to that stopping point, and so on. I can't figure this one out, though.
optimization puzzle
$endgroup$
You have been given the task of transporting 3,000 apples 1,000 miles
from Appleland to Bananaville. Your truck can carry 1,000 apples at a
time. Every time you travel a mile towards Bananaville you must pay a
tax of 1 apple but you pay nothing when going in the other direction
(towards Appleland). What is highest number of apples you can get to
Bananaville
The answer is $boxed{833}$. However, I don't understand how to obtain this answer. Also, is there any way to show that the answer is optimal?
I have seen a riddle similar to this before, and I think the trick is to move $1000$ apples towards a stopping point, come back, get more to that stopping point, and so on. I can't figure this one out, though.
optimization puzzle
optimization puzzle
asked Jan 17 at 20:11
user614735
$begingroup$
Doing a quick Google search will get you a method for $833$. See for example goodriddlesnow.com/riddles/hard/page:5/sort:Riddle.difficulty/… . This doesn't prove optimality though
$endgroup$
– pwerth
Jan 17 at 20:22
add a comment |
$begingroup$
Doing a quick Google search will get you a method for $833$. See for example goodriddlesnow.com/riddles/hard/page:5/sort:Riddle.difficulty/… . This doesn't prove optimality though
$endgroup$
– pwerth
Jan 17 at 20:22
$begingroup$
Doing a quick Google search will get you a method for $833$. See for example goodriddlesnow.com/riddles/hard/page:5/sort:Riddle.difficulty/… . This doesn't prove optimality though
$endgroup$
– pwerth
Jan 17 at 20:22
$begingroup$
Doing a quick Google search will get you a method for $833$. See for example goodriddlesnow.com/riddles/hard/page:5/sort:Riddle.difficulty/… . This doesn't prove optimality though
$endgroup$
– pwerth
Jan 17 at 20:22
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The truck should be as full as possible, so as soon as you can combine multiple truckloads into one, you should do so. The first time that happens is after 333 1/3 miles. You can get the apples to the 333 1/3 mile marker in 3 truckloads, pay 1000 in tax, and be left with 2000 apples. Then you can go another 500 miles before you can combine truckloads again. Hauling 2000 apples in two truckloads over 500 miles costs you 1000 in tax, leaving you with 1000 apples at the 833 1/3 mile marker. The remaining 166 2/3 miles can be driven with one truckload, leaving you with 1000-166 2/3=833 1/3 apples.
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
$endgroup$
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3077458%2fmath-optimization-riddle%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The truck should be as full as possible, so as soon as you can combine multiple truckloads into one, you should do so. The first time that happens is after 333 1/3 miles. You can get the apples to the 333 1/3 mile marker in 3 truckloads, pay 1000 in tax, and be left with 2000 apples. Then you can go another 500 miles before you can combine truckloads again. Hauling 2000 apples in two truckloads over 500 miles costs you 1000 in tax, leaving you with 1000 apples at the 833 1/3 mile marker. The remaining 166 2/3 miles can be driven with one truckload, leaving you with 1000-166 2/3=833 1/3 apples.
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
$endgroup$
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
add a comment |
$begingroup$
The truck should be as full as possible, so as soon as you can combine multiple truckloads into one, you should do so. The first time that happens is after 333 1/3 miles. You can get the apples to the 333 1/3 mile marker in 3 truckloads, pay 1000 in tax, and be left with 2000 apples. Then you can go another 500 miles before you can combine truckloads again. Hauling 2000 apples in two truckloads over 500 miles costs you 1000 in tax, leaving you with 1000 apples at the 833 1/3 mile marker. The remaining 166 2/3 miles can be driven with one truckload, leaving you with 1000-166 2/3=833 1/3 apples.
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
$endgroup$
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
add a comment |
$begingroup$
The truck should be as full as possible, so as soon as you can combine multiple truckloads into one, you should do so. The first time that happens is after 333 1/3 miles. You can get the apples to the 333 1/3 mile marker in 3 truckloads, pay 1000 in tax, and be left with 2000 apples. Then you can go another 500 miles before you can combine truckloads again. Hauling 2000 apples in two truckloads over 500 miles costs you 1000 in tax, leaving you with 1000 apples at the 833 1/3 mile marker. The remaining 166 2/3 miles can be driven with one truckload, leaving you with 1000-166 2/3=833 1/3 apples.
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
$endgroup$
The truck should be as full as possible, so as soon as you can combine multiple truckloads into one, you should do so. The first time that happens is after 333 1/3 miles. You can get the apples to the 333 1/3 mile marker in 3 truckloads, pay 1000 in tax, and be left with 2000 apples. Then you can go another 500 miles before you can combine truckloads again. Hauling 2000 apples in two truckloads over 500 miles costs you 1000 in tax, leaving you with 1000 apples at the 833 1/3 mile marker. The remaining 166 2/3 miles can be driven with one truckload, leaving you with 1000-166 2/3=833 1/3 apples.
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
answered Jan 17 at 20:26
LinAlgLinAlg
10.1k1521
10.1k1521
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
add a comment |
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
how do i show this is optimal?
$endgroup$
– user614735
Jan 17 at 21:31
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
$begingroup$
@stackofhay42 the rationale is in the first sentence.
$endgroup$
– LinAlg
Jan 17 at 21:44
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3077458%2fmath-optimization-riddle%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Doing a quick Google search will get you a method for $833$. See for example goodriddlesnow.com/riddles/hard/page:5/sort:Riddle.difficulty/… . This doesn't prove optimality though
$endgroup$
– pwerth
Jan 17 at 20:22