PLEASE HELP ME TO SOLVE THIS PROBLEM,I REALLY CAN'T DO IT!!!!!!!!!!!

THOMAS GOES TO THE BIRTHDAY PARTY OF HIS FRIEND & FOUND THAT THERE ARE 3 GUESTS WHO HAVE B'DAY ON THE SAME DAY OF THE WEEK & IN THE SAME MONTH OF THE YEAR.HE ALSO FOUND THAT ALL THE GUESTS WERE BORN IN THE FIRST SIX MONTHS OF THE YEAR.FIND THE LEAST NO. OF PEOPLE INCLUDING THOMAS AT PARTY. . . . ANSWER IS '85' HOW TO GET ANSWER ? PLEASE HELP ME!!!!!!!!!!

#JustForFun #Difiicultprobs

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

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}`	$\boxed{123}$

Comments

There are 6 different months and 7 different days of the week, so there are 42 different possible combinations of a month and a week. For there to be 3 of the same month and same week, by Pigeonhole principle there must be at least $42 \times (3-1)+1=85$ people.

Joel Tan - 7 years, 5 months ago

please what is piegon hole principle ???????????????????????????

Harsh Shrivastava - 7 years, 5 months ago

Pigeonhole principle states that if x pigeons are placed into y pigeonholes, one pigeonhole must contain at least 2 pigeons if x>y.

Or generally, for your question, this version is better: if there are x pigeons and y pigeonholes, one of the pigeonholes must contain at least n pigeons where n is the smallest integer larger than x/y.

It can be proved by contradiction: suppose that all pigeonholes contain less than n pigeons. Then each pigeonhole contains less than $\frac{x}{y}$ pigeons. However, since there are y pigeonholes the total number of pigeons is less than x, contradicting the fact that there are x pigeons.

So in your question, there are 42 different 'pigeonholes' as mentioned above. Also, by the above, the smallest integer larger than $\frac{number of people}{42}$ is 3. So the fraction must be larger than 2 so the number of people is greater than 84, so 85 is minimum.

Joel Tan - 7 years, 5 months ago

@Joel Tan – thanks a lot !

Harsh Shrivastava - 7 years, 5 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}`	$\boxed{123}$