Easy math puzzles

Original solution still valid, but here’s a more efficient way to get 14.
The last math puzzle (beer jugs) also used fives and sevens as the only valid inputs. Coincidence??

What, nobody's going to try the negative root?

The problem says you’re using a calculator. Show me a calculator that gives a negative value for a square root.

Also, how does √ 5+5+5+5+5= -5 ?

Quote: Ace2

The problem says you’re using a calculator. Show me a calculator that gives a negative value for a square root.

Also, how does √ 5+5+5+5+5= -5 ?
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The ASCII radical sign available here, that's just how it looks, no way to extend it over the whole statement. I suppose I should have used parentheses.

And I'll show you a calculator that gives a negative square root when you show me one that can only add 5 and add 7 and take square roots! This is a very unusual calculator to begin with, and unless stipulated we can make no assumptions about which square root.

All submitted answers look correct. Well done group!

I got this one from one of my puzzle videos from the Ted-Ed YouTube channel. This one is titled, "Can you solve the giant cat army riddle? - Dan Finkel"


Direct: https://youtu.be/YeMVoJKn1Tg?si=RCtKeyqbfmB5oj0J

This is more of a math question than a math puzzle.

In the game of craps, many casinos charge a 5% commission (of the bet amount) on a win only when buying the 4/10.

My understanding is that a $40 lay bet on 4/10 would win $59 for $40 at a casino that collects the commission on win only. But this doesn’t seem right since a lay bettor would be paying twice the $vig as a buy bettor in the long run.

If laying the 4/10, shouldn't the casino charge the 5% (of potential win amount) on a LOSS only? For example, if laying the 4 for $40 to win $20, you'd actually lay $41 to win $61 for $41.

This would ensure the casino makes the same $ vig on a player laying the 4 for $41 as a player buying it for $20. In a casino that charges the vig up front, they make the same $vig on a $20 buy and a $40 lay, so that seems to be the intent.

Quote: Ace2

This is more of a math question than a math puzzle.

In the game of craps, many casinos charge a 5% commission (of the bet amount) on a win only when buying the 4/10.

My understanding is that a $40 lay bet on 4/10 would win $59 for $40 at a casino that collects the commission on win only. But this doesn’t seem right since a lay bettor would be paying twice the $vig as a buy bettor in the long run.

If laying the 4/10, shouldn't the casino charge the 5% (of potential win amount) on a LOSS only? For example, if laying the 4 for $40 to win $20, you'd actually lay $41 to win $61 for $41.

This would ensure the casino makes the same $ vig on a player laying the 4 for $41 as a player buying it for $20. In a casino that charges the vig up front, they make the same $vig on a $20 buy and a $40 lay, so that seems to be the intent.
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If you are betting 41 against the casino's 20, that's a commission of 2.5% (1/40) on the entire bet, win or lose.

Quote: ThatDonGuy

If you are betting 41 against the casino's 20, that's a commission of 2.5% (1/40) on the entire bet, win or lose.
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That's incorrect. A 2.5% commission of the lay amount (paid on win or loss) would pay $60 for $41 on a win since the $1 commission is never returned. That's a house edge of 1 - 2/3 * 60/41 =2.44%. It doesn't work out to exactly 2.5% since the $1 commission is added to the bet instead of subtracted from it.

However, when the 2.5% commission is paid on loss only, a win pays $61 for $41 for a house edge of 0.81%

The casino calls these a 5% commission on the potential win amount instead of 2.5% on the lay amount