In college, I noticed that my roommate counted things in chunks of three. I had only ever counted items either individually or in chunks of two, but for most physical items I count, there are fewer than 50 of them, and counting by 3s up to that number is about as easy as counting even numbers. I was surprised to see that visually identifying three of an item was not harder than going by twos. Of course, it's also faster to count by 3 than by 2.
I'd be interested to know if others count by 1, 2, 3, or something else. (Another trick I learned working retail is to count out X coins, stack them vertically, and then make more stacks of the same height. Much faster than counting them all out individually!)
> The accuracy, speed, and confidence with which observers make judgments of the number of items are critically dependent on the number of elements to be enumerated. Judgments made for displays composed of around one to four items are rapid,[2] accurate[3] and confident.[4] However, as the number of items to be enumerated increases beyond this amount, judgments are made with decreasing accuracy and confidence.[1] In addition, response times rise in a dramatic fashion, with an extra 250–350 ms added for each additional item within the display beyond about four.[5]
I can't spot the references I thought I'd see here but I recall there being work around training this and seeing people improve up to around 7-8.
I've always counted in 5s, or really more like a 3+2 or 2+2+1. The garden party for me is keeping the number in my head so knowing the last digit is always 0 or 5 makes it easy. Then you just add the remainder at the end.
That's roughly how you count change too.
Ex: if I were to count 21 items my mental count would be 2,3 [5] 3,2 [10] 2,2,1 [15] 2,3 [20] and 1. [21]
For bills and coins, I count by object, not denomination. Then multiply total by denomination.
For counting large numbers of bills, I like creating stacks of 20. Then I count the number of stacks. After that I make stacks of 100 bills, and wrap them. In this way, I am never 75 bills deep, lose count and have to restart.
I know I have to count each stack of twenty twice, and ideally not three times, so I count 21 bills out, then if its 21 the second time, I take one off.
For piles of coins(and socks, et al), remove the most common/visible/largest type. For example, I would remove $1 coins into their own pile/bag, not bothering to count yet. Then as they become less obvious, I switch to $2 coins, then $0.25, then $0.05(since they are larger than $0.10 coins).
I had an electronic coin counter, but away from the office, that's how I sorted coins. If I wanted to count on site, it was a lot easier to count homogeneous bags. I could also weigh for a rough estimate.
> I know I have to count each stack of twenty twice, and ideally not three times, so I count 21 bills out, then if its 21 the second time, I take one off.
I'm not sure I understand this. Is it just so you don't have to hunt for an extra bill somewhere else? If the second count doesn't match the first count you need to count a third time anyways, right? It sounds like you're implying using a 21 stack initially reduces recounts.
Very interesting — I'd like to try this. Do you have any sense of whether this is as reliable as counting by one, two or three? That is, if you were counting out something really important, would you do it this way? Was there much of a learning curve?
I'm not kjeetgill, but I also group things visually in 5 when counting.
On your question, I feel less confident in my count, the more things I have to count. Since there will always be fewer groups of 5 than groups of 1, I always feel more confident counting in groups of 5 than of 1.
EDIT:
It's like divide and conquer. You divide the work by first making sure each group has only 5 items by glance counting (what kjeetgill means with 2 + 3), and then you count the groups, and add what didn't fit in any group.
Having the work divided like this makes it easier to verify that it was all done correctly. You'll end up feeling more confident about some groupings than others (because of the way the items are positioned) and you'll just want to recheck the ones you're not so confident about and readjust accordingly. Once you're confident in the groupings, you can recount the groups more easily than having to recount each individual thing.
For most sums, you'll end up adding less than 5 or 10 things at each step, which is easy.
I think its advantage is reliability. I don't know if it does much for speed.
You can't make off by 1 or 2 errors because then you'd end up with a count like 23 or 27. You're counting by 5... the last digit needs to be 0 or 5! And you're not going to make an off by 10 error.
You can visually pick out 2s and 3s to make your 5 before you add them in.
In my experience, you can make off by 1 or 2 errors when you accidently include 1 or 2 items in different groups of 5 at the same time. You end up with 25 when you should have ended up with 23. It may also happen that you don't include 1 or 2 items in the groups, because you thought you'd already included them, while visually scanning the area. When that happens, you end up with 25 when you should have ended with 27.
Another trick I learned working retail is to count out X coins, stack them vertically, and then make more stacks of the same height. Much faster than counting them all out individually!
I do a similar thing when counting "manipulable" objects of the same size --- in semi-binary. I make a stack of height n, then another, and stack them on top of each other to create one of 2n, before making another of 2n. If there aren't enough, I use the next-lower power of 2, and so on. Then I add them all together at the end and it's usually faster for me to go from binary -> hex -> decimal than do the additions in decimal. Memorably, I once skipped the last step while tired:
coworker: how many?
me: E6.
coworker: huh?
(several more seconds later)
me: ...oh, I mean 230.
I worked in a bread shop 6 days a week for several months, and my principle duty was to arrive at 630am and count the cakes in big trays that were unloaded from a van.
By the end of that, I could count up to about 18 donuts just by looking.
This is discussed in The Universal History of Numbers, by Georges Ifrah.
You better check the book, because it has been a long time since I read it, but he explained that most people counts 3 by 3, sometimes 2 by 2, and exceptionally 4 by 4. Only very exceptionally people can count 5 by 5. What most of us do when counting 5 elements, is to divide them in a chunk of 3 and one of 2.
I count in 3's because that's how I was taught to count newspapers when I was a paper boy. I didn't really question it but you're quite right that it's just as easy to see 3 items as 2, and it's faster. You just have to get used to the sequence but that's much easier than remembering all the multiples of 3. Our brains are great at remembering the next item in a sequence even if we can't randomly access them very well.
I usually count variable-length things in fours. Try counting the words as you read a paragraph. Three is too inefficient, five is a bit too much for my eyes but four is just about right.
Of course, counting items with fixed dimensions like coins or bottles, you group them appropriately in piles of 5 or 10 or 12 or 16 depending on the "natural" layout, and multiply from there.
I have always counted groups of things in threes, cards most commonly. The patterning takes more practice to get used to because the last digit doesn't repeat the way it does when you count by twos.
I also count coins by 5s if I have a bunch of them flat on a table - it's faster that way.
> I'd be interested to know if others count by 1, 2, 3, or something else.
I count in 1,2,3,4 or 5 blocks depending on the situation. For example if I am supposed to have 13 buttons and I want to verify it. I visually or physically separate 5, then another 5 and then check the remaining buttons. If it is 3, then I have verified it.
Anything above 5 gets harder and harder to distinguish. I could easily and naturally spot 1, 2, 3, 4 or 5 items. But if it gets higher than that, it gets harder for me to distinguish between a group of 7 or 8 or 9 items.
I'd be interested to know if others count by 1, 2, 3, or something else. (Another trick I learned working retail is to count out X coins, stack them vertically, and then make more stacks of the same height. Much faster than counting them all out individually!)