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# 3 Men and a little ladder

## Question

3 men: Arnold, Bryan and Colin decide to purchase a ladder between them.

They each contribute 5 coins and give these 15 coins to David who is going to purchase the ladder for them.

David buys the ladder for only 10 coins and feels guilty about keeping all 5 coins change.

He decides to give one coin each back and keep only 2 for himself.

On giving one each back this means that Arnold Bryan and Colin have now spent 4 coins each and David kept 2

3x4=12

Davidâ€™s share of 2 coins means a total of 14

But we started this question with 15 coins where did the other one go?

I will not accept quantitive easing as a solution. LOL

## 18 answers to this question

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If he gives each two back, he keeps three for himself, not two, thus the problem statement is invalid

A much better version of this puzzle has been posted using a hotel and busboy scenario that introduces a fourth party. This puzzle is directly clear.

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The calculation should be: original sum =15. cost =10 rest 5.

Reimbursed 3 X 1 =3. Commission =2.

So one has Original sum 15 - cost (10) - Reimbursement (3) - Commission (2) = 0 !

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If he gives each two back, he keeps three for himself, not two, thus the problem statement is invalid

A much better version of this puzzle has been posted using a hotel and busboy scenario that introduces a fourth party. This puzzle is directly clear.

If he gave each 2 back he would need to return 6 yet only has 5

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It says that Arnold, Bryan and Colin have only spent 4 coins each and Daniel kept 2. e.g 3x4=12,+ 2=14

Arnold, Bryan or Colin have actually spent only 3 coins each because they each got one back: 3x3=9

The three of them kept 1 coin each: 3x1=3

Daniel kept 2 coins: 1x2=2

The two coins Daniel kept were from two of the other three. e.g Arnold & Bryan. The remaining coin is from one of the other three. e.g Colin

3x3=9, so the missing coins must havin(g been spent on the ladder: 9+1=10

I hope this isn't too confusing, I couldn't find a way to put it into context. LOL)

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they spend \$12, ladder only costs 10\$, so daniel keeps the extra two. there is no reason to add 2 to 12.

ps i <3 you asdf

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There are no missining coins because David contributed nothing. Arnold, Bryan and Colin each paid 4 coins of that 10 went for the ladder and 2 were kept by David. Perhaps as a commission? 10 for the ladder + 2 for David = 12 coins

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But initially 15 coins were on the playing field. Now there are only 14. One must have gone somewhere

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So...

The ladder real price, divided for the three, is 3,333(3).

Because there isn't 0,333(3) coins, one of the coins had to be spent to pay the ladder : 0,33(3)*3=1 coin

So, one of the coins from one of the people had to be spent to pay this decimal part of the price.

We can't use a determined number of coins equal from each buyer. There is one of them that will have to spend one more on this buying.

(of course, the rest of the problem covers the whole problem of these)

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The other coin went towards the ladder because:

2 for David

3 for Arnold, Bryan and Colin (one for each)

10+2+3=15

Therefore there is no missing coin.

(Earlier when I said Daniel it was meant to be david. LOL)

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the 3 guys paid 3x4=12 10 for the ladder and 2 to david ..... so simple

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oh well at least it has got me introduced to the site. Well done all

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This is how it made sense to me.

When the statement says. The boys have spend 4 dollars each to a total of \$12 PLUS David's share is equal to 14, is wrong.

Because we can't add David's share to the \$12; David's share comes from the \$12 and is part of it.

You can say the same thing as ridicilous as it sounds: each have spend 4 dollars to a toal of \$12 plus the \$10 that the store keeper has for the ladder equals to \$22. Where did the extra \$7 go ? well 2 went to David. So where did the other \$5 go ? you see what i mean ?

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FWIW I liked the puzzle. Cleverly worded to confuse. Nice one.

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Arnold, Bryan and Colin payed 12 coins for a 1O coin ladder (3x4) because they employed a middleman who charged a 2 coin commission.

Its just a good thing that David had a conscience otherwise they might have been left thinking that 15 coins was good price for a 10 coin ladder and "by the way where's that ladder?"

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There is no missing coin. The question itself is flawed. You don't take the amount contributed by each party (3 x 4 = 12) and ADD the two that David kept! You take the amount contributed by each party (3 X 4 = 12) and SUBTRACT the two kept by David which leaves the 10 (ten) coins that were spent on the ladder. The math is all good, its the question that is illogical.

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10 + 2 is the mistake in calculation .

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1.

Since each paid \$4. So, total spent 3*4 = 12

So, left over money = \$12 - \$10 = \$2, which was kept and not distributed.

2.

Since collected sum was \$15.

Returned amount was \$1 each(3*1 = \$3)

Left Over is \$2

So, equation is: \$15 = \$10 + \$3 + \$2, which is true

3.

Suppose, we don't have anything to buy.

3 fiends gave \$5 each(\$5 * 3 = \$15)

They were returned \$1 each(\$1 * 3 = \$3)

Left over is \$12

Everone's spending: \$5 - \$1 = \$4

So, now equation is:

\$15 - \$3 = \$4 * 3, which is correct

Edited by Swaraj

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I think we should get rid of the 10 used to buy the ladder, because no one can have that back. Then since the change was 5, the middle man kept two, and gave each of the contributing men 1. 3+2=5, then if we had to, we could take the 10 and say 5+10= 15, which is how much they started with.

Edit: (5:16 PM, 1/24/12)

Another thing that it could be, is because the three men spent a total of 12 coins, 10 for the ladder, 2 for David. The total the three men spent should include the 2 coins for David.

Edited by Monty55

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