Object Picking

For problems like:

JimmyBobJoe has 8 red things, 7 blue things, 5 pink things, and 4 white things. What is the least number of objects he must pick to ensure having exactly 4 of each object?

Would it be 8+7+5+4 or 4+5+7+4?

And if the problem read: JimmyBobJoe has 8 red things, 7 blue things, 5 pink things, and 3 white things. What is the least number of objects he must pick to ensure having exactly 4 of a thing?

Would it be 13?

I always confuse myself on these things!

#Pickingobjects

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

Use the worst case scenario. He needs to pick 10 for the first case ( 3 colors each for the worst case and 1 more of either each color) and for the second scenario, it would be 13 ( 3 colors from each and one more from either of the 4 colors) .

Venture HI - 7 years, 2 months ago

I miswrote question #1 and it should read "to ensure picking 4 of each object."

So shouldn't it be 8+7+5+4 and not 10??

Asher Joy - 7 years, 2 months ago

Let me get the question right. You have 8 reds, 7 blues, 5 pinks, and 4 whites. Question. What is the least number of objects he must pick to ensure picking 4 of the same color. Answer: Consider the worst case scenario. You picked a red, a blue, a pink and a white. Next round, you did the same. Third round , you did the same again. Now, you ended up having 3 of each colors; 3 reds, 3 blues, 3 pinks, and 3 whites. Talk about bad luck. So, your next pick of any color should get you or ensure a 4 of each color. Total= 3 reds+3blues+3pinks+3whites+ ( 1 of any of these colors)=13

Venture HI - 7 years, 2 months ago

@Venture Hi – Yes...I understand that for question #2...but I'm talking about #1. JBJ has to pick 4 of EACH object...

Sorry for the misunderstandings.

Asher Joy - 7 years, 2 months ago

I read the question wrongly. For both cases the number of picks should be 13.

Venture HI - 7 years, 2 months ago

yes, it is 13

Kushagra Sahni - 7 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$