“If a chicken and a half can lay an egg and a half in a day and a half, how long does it take a grasshopper with a wooden leg to kick all of the seeds out of a dill pickle?”
My Grandpa used to pose that to us from time to time. No one, to this day, has found the answer! ;)
Kind of like Trump Derangement Syndrome on Congress.
1 4 2 7 22 11 34 17
2 1 ....
3 7 ,...
4 ....
5 16 8 4 ....
6 3 ...
7 ....
8 4 ....
9 28 14 7 ....
Ok so now we know why they picked Q!
Thanks for posting this! Very fascinating.
I’d never heard of a mathematical “conjecture” before.
I sent this to my math teacher sister. She teaches middle school kids in Baltimore who still struggle mightily with the concept of “one-half” after a full year of math instruction.
Is 0 a number? If it is, this thing calls apart really quickly.
Do all resolve to 1 ? Enough that you can stop now. Or, save time and DON’T multiply by 3. See? Yep, all.
“If it’s odd, multiply it by 3 and add 1. If it’s even, divide it by 2.”
At first glance, the process would seem to yield even numbers oftener than odd ones. Those get divided by 2, so the series would seem to trend downward to 1, eventually. Must be more complicated than that, though.
“Almost” doesn’t work with mathematics.
No thanks. Not into self-imposed tedium.
Think of it as starting with 5. It's even, so multiply it by 3 (which makes 15) and add 1 (which makes 16). 16 is a power of 2 because it's 2 to the 4th power. Basically, from this point on you're halving it over and over until you get to 1. So: because 16 is even you halve it to get 8 (which is 2 to the 3rd power), then halve it again to get 4 (2 to the 2nd power), then 2 (2 to the 1st power), then 1 (2 to the 0 power).
Simple conjecture that any lay person can understand has baffled mathematicians for decades.
*”*”*”*”*”*”*”*”
BINGO!!
Most anyone in retail understands this. It is encountered daily where one has to deal with mark-up and mark-down.
Now give every supermarket manager his or her PhD.
It’s the proof that eludes us.
The problem is fascinating, and simple to express, and really comes down to two questions:
First, are there any numbers other than 1 which, if multiplied by 3 and then adding 1, and then dividing by 2, yield the same number.
Second, are their any repeating sequences of numbers where, having done those same calculations, you end up in a loop.
The 3rd, more esoteric question, is whether there is a sequence that never repeats, but also never leads to 1 — but given an infinite number of tries, this must necessarily either be proven false, or fall into the 1st or 2nd questions.
Seems so simple and obviously true but the devil is in that ‘take any number’ (assumed to be a positive ‘whole’ number - if that’s not to be assumed THEN all bets are off immediately anyway)’
I suspect that there possibly there are whole numbers that when that process is applied form a loop with numbers going back up to the loop start number OR even there are patterns of an infinite upward ramp — AND PROVING THAT THAT DOES NOT HAPPEN (for ANY number upto Infinity ) IS THE HARD PART... (so to not always lead to the final ‘1’)
Any number ...
Consider a possible convolution — consider the ‘mult by 3 and add one’ creates an even (a bigger number) which subsequently being even gets ‘divided by 2’ (a less small number than originally) but still is an even - numbers like 10 but when divided by 2 become odd again.