Lay the five ‘Birthday Number’ cards on a table or floor in front of your group.
Ask your group to study the numbers on the cards.
Invite one volunteer to tell you which one or more cards has their birth date on it (not month or year.)
Applying a simple solution (refer Narrative tab,) you easily predict their birth date accurately.
After several successful predictions, ask your group to identify what it is you’re doing to solve the puzzle.
Within five or so minutes, and after giving a couple of clues, reveal the solution to your group.
Video Transcript for Birthday Numbers presented by Mark Collard
So here’s your objective now folks. Is that every number one to thirty-one, has been printed on each of these five cards. But clearly each card has only sixteen numbers.
So there’s a reason why only the sixteen numbers that appear on each of these cards occur. But note that all the numbers are from one to thirty-one.
When you think of thirty-one, what does it immediately come to mind of? So you think thirty-one, what comes in thirty-one’s?
(End of the months?)
A month. Okay, so, I am so smart. I know I’m trying to flatter myself here. But the object is that I know without a doubt the birth date of you. By simply you telling me which one or more of these cards your birth date occurs on, I will tell you what your birth date it.
For example, I’m born on the twentieth, so I’m kind of giving this away. But on the twentieth, the number 20 only occurs on the cards… which is it? C and E.
C and E. It does not appear on A. B. or D.
All you need to tell me is the letter of the cards, one or more cards, in which your birth date occurs on and I will tell you what your birthdate is. So not including the month it’s just your birth date.
Who would like to start?
Okay. You got it. Jillian or… who? Go for it.
(Uh, card B)
Just B? So you’re the second? No, then definitely, your number is on another card then.
Go for it.
(E and B)
A and B?
(E, E and B)
Oh, E and B? Great you’re the eighteenth.
No? Then your number is appearing on another card.
(A and B)
You’re just A and B? You’re the 3rd.
Okay. Yeah, Jen?
Just D? You’re the 8th.
(C and D)
C and D? These two here? The 12th. Am I correct?
Oh, then your number appears somewhere else.
(A, C and D)
A, C and D? The 13th.
Now at this point you’re going “Wow, he’s amazing.” And that’s an appropriate response. Or you can now try and work out “What the heck is he doing?”
There are two ways of doing this. One is extremely complicated, it was described to me once and I have forgotten how it’s done.
The other one, grade two kids get within about three minutes. So I can tell you right now, you’re thinking way too hard. So there’s something very simple about this.
So the object is to identify “what is it that I’m doing” and it’s not a memory test.
How do I know with certainty what your birth date is by you just telling me the one or more cards on which your birth date occurs?
You will all know the solution to this within a couple of minutes. Okay, so if you’ve got a theory, if you can work on something, go for it.
So again, would someone like to give me an idea?
(C, D and E)
So, C D and E? Those three? The 28th.
(A and C)
A and C these? The 5th. Correct?
Okay, now I think we’re all good now, he’s just discovered his birthday.
(Laughs at Birthday Numbers puzzle)
So now, start to look. I’m not even looking at the cards now. So it’s not necessarily a memory trick. The reason I’m not looking is that I’ve done this a lot. However, for your purposes you do need to look a the cards. There is an answer staring you in the face. As I’ve said, adults get this much longer after kids. So you’ll be seeing something, there’s something important.
So here’s a couple of clues for you.
(Where’s the 16?)
The 16 is definitely there.
There is a number that appears on every single card.
Alright, there’s a reason for that. There are also a series of numbers that only appear on one card. Which numbers are they?
No. So… we have one number that appears on all cards. And we have five numbers I think you gave me that appear just on one card. Okay, you now have everything you need to know to solve the problem. Even though it’s not obvious to you. The truth is always obvious to those who know it.
What you got Mel?
(We both thought that if it was A and B, then it would be the 3rd)
It would be. Do you know why?
(Because the first…) Okay, so let me just test your theory because it will help in terms of other people. So I think you’re onto it.
If I said I was B and D, what number am I thinking?
Okay, you’ve got it. You’ve got it correct. So whatever you’re doing is working, lets see how many people can now pick it up.
So we identified a moment ago, five numbers that only appear on one card. For example, what’s the only number that appears on A?
Because it doesn’t appear on any other card. Note where the one is.
What’s the only number that appears on B?
Okay, anything that might connect?
(I think C’s would be four, would it?)
It is! What about D? What’s the only number that appears on D and no other card?
Okay, there’s something they all have in common.
(So you’re adding up the numbers?)
Okay, so for example, you might be working on a suggestion here.
If I was A. B, C and D… what number am I thinking?
(You are born on the 3rd, the 7th… the 15th.)
The 15th, well done. Exactly, you have a good system.
I’m about to reveal the system, if you don’t want to know <makes noises> go like that, just for a moment. Does anyone else want to test a theory before I start?
You got a theory you want to test?
(Oh no no…)
You’re ready? You’re ready, okay great. So what is the thing they all have in common, the numbers, that only appear on one card? What’s the thing they have in common?
Apart from the fact that they are power to the two of something.
(The same font?)
The same font?
That’s great. That’s an adult, a great example of an adult thinking too hard.
What else to all the numbers, 1, 2, 4, 8 and 16 have in common?
No, they’re not all even.
Same spot, what do you mean by that?
(Top left hand corner.)
Top left hand corner. So if I said to you “I’m thinking the numbers, uh the cards A and C, what number am I now thinking?
Five. Why is it five?
(One plus four.)
One plus four equals five. Now that as I said is one of the two solutions. There was a reason why the number one appears here and the number four appears there. That’s the other more complex mathematical solution, which I forgot three seconds after it was explained to me. There is a reason why the particular numbers appear on certain cards.
So, here it is folks. It’s not a memory test, but is is the first number of each of the cards. So the reason the number 31 appears on all of them, is that you need all of the numbers added up makes 31. If it was just these four they add up to what?
Fifteen. One plus two plus four plus eight equals fifteen. Plus sixteen gives you thirty-one. That’s the trick. There was a particular reason why these numbers appear in the particular order in which they are. Has everyone got the system first of all?
Anyone not? It’s okay to say you don’t. Okay, cool.
(So you can just add any of the numbers into it…)
It won’t work, no. There’s a reason, that’s that other solution which I can’t describe.
And for other people’s purposes, when you gave me the letters that matched your birth date…
So if I… I’m on the 20th, so I know I’m C and E. Because twenty only appears on these two cards. Four plus sixteen equals twenty. There’s a reason for that, and that’s that other solution I can’t describe.
But, this is the easy one, that’s why kids pick it up quicker. They’re not trying to think it too hard, they just look at something that’s in common. A group of grade 2 kids taught me this activity. They had been taught it in class and I love using it with adults because we often think about it too hard.
I couldn’t see it and the kids could. It’s pretty wild.
(group continues with Birthday Numbers exercise…)
How To Play Narrative
A group of second grade students showed me this exercise many years ago, and it attracted my attention immediately. Like many lateral-thinking puzzles, it is frustratingly intriguing.
Start by laying the five cards (available in Resources tab) in order – A B C D E – on a table or on the floor in front of your group. Every card has 20 numbers on it – all of them chosen from 1 to 31, hence the birth date connection.
Ask your group to study the numbers on the cards, and when someone is ready, invite them to tell you which one or more of the five cards has their birth date (as distinct from the month and year) on it. Their date will always appear on at least one card, and maybe on all five cards.
Let’s say the first volunteer tells you that her birth date appears on three cards, A, B and D. You then proceed to stun the room by immediately predicting that their birth date must be the 11th of the month.
After a few accurate predictions like this, the room will start to buzz with the familiar “Wow, how does he/she do that?” Which is the whole point of the exercise – you would like your group to figure out how you do it.
At this point, explain to your group that to solve this problem/puzzle, they need to think laterally. There is something very obvious that will easily help someone in the know to solve the puzzle every time, and quickly. Encourage your group to test some ‘theories’ and see if they fit with your answers.
After a few minutes, and many failed attempts to find a solution, you will more than likely need to share some clues:
What numbers only appear on one card?
What number or numbers appear on every card?
What relationship do these numbers have in connection to each other?
One by one, the group will start to pick-up on the solution, which was staring them in the face all the time of course!
Now, don’t read on if you would prefer to work this out for yourself, because here comes the solution…
The number which appears in the top left-hand corner of each card is the key. The solution is always the sum of these (top left-hand corner) numbers of the nominated cards.
Using the example quoted above, if the cards are A, B and D, the solution is 1 + 2 + 8 = 11. So the participant’s birthdate is the 11th of the month! It’s that easy (if you know it.)
Practical Leadership Tips
As with all lateral-thinking puzzles/exercises, use sparingly and always, always, with care. In my experience, many people have been scarred in the past from one or more tortuous experiences with ‘lateral thinkers,’ often because the solution didn’t come quickly, and/or one after another, they were always the last one to get the solution. Therefore, only use one or two at a time, and always ensure that you solve the puzzle within a short time frame.
This is one of those exercises that I often start quietly in the corner with just a couple of people, and then slowly, more and more people gravitate toward us. Within minutes, I’ve got everyone’s attention.
Unless you’re good at the mathematics behind the numbers and choose to create your own cards, you are better off downloading the Birthday Numbers cards from the Resources tab. Print the five cards and paste them to index cards for longevity.
It really doesn’t matter in what order you place the cards in front of your group. The solution is the same, but you give your group a fighting chance to solve it if they are sequenced A to E.
There is a particular reason why every number appears on each card. It’s rather mathematically involved, and I forgot the formula about three seconds after having it explained to me. So, just focus on the top left-hand numbers of each card, okay?
You could integrate this Birthday Numbers game as part of a well-designed SEL program to develop your group’s abilities to demonstrate self-discipline as much as promote personal and collective well-being.
Specifically, this activity offers opportunities to explore and practice the following social & interpersonal skills:
Linking Feelings, Values & Thoughts
Having A Growth Mindset
Controlling One’s Emotions
Demonstrating Self-Discipline & Self-Motivation
Taking Other’s Perspectives
Demonstrating Empathy & Compassion
Demonstrating Curiosity & Open-Mindedness
Promoting Personal & Collective Well-Being
You can learn more about SEL and how it can support character education here.
Health & Wellness Programming
There is no specific health & wellness perspective to this activity other than promoting the benefits of working with others to solve a problem.
In a small way, you could argue that the focus required to successfully crack the code speaks to the benefits of being mindful. You could also invite your group to explore issues of resilience because, for many people, this will be a very frustrating exercise that they may want to quickly give up on. In this latter case, focus on what it took to remain engaged and focused on the problem rather than the mechanics of the actual solution to help your group acknowledge and practice certain useful coping strategies.
If you can think of more explicit ways in which Birthday Numbers could be purposefully integrated into a health and wellness program, please leave a comment at the base of this page.
Sixty-Three Number Mystery Calculator: There is a 63 number version of this exercise that is spread across six cards. Same concept with more numbers. Contact playmeo if you are interested in getting your hands on a copy.
Open the Virtual Adaptation tab to learn how to present this activity online.
In advance, create a PDF or PowerPoint slide which displays all five Birthday Numbers cards on one screen. Share this with your group and proceed as normal. With all cards on the screen, it is still possible to ask one or more volunteers from your group to lead the exercise (with your group) if they have identified the key successfully.
If a small number of participants crack the code early, divide your group into various breakout rooms (with 2 to 5 people) and assign each of these early-birds to one of the rooms to lead the exercise with a smaller group.
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Useful Framing Ideas
Some people will love this next activity, and yet, there will be others of you who will immediately be turned off because I’ll use the words ‘lateral-thinker.’ [pause for groans] However, my commitment to the group is this – everyone of you will know the solution to this exercise within the next four to five minutes. So, hang in there, and know that this won’t take too long. Indeed, you may even surprise yourself, so be open to possibility…
Describe to your group that you possess very special magical powers, and can predict with 100% accuracy the date of someone’s birth. Indeed, if you can memorise the top left-hand numbers which appear on each card (eg A=1, B=2, etc), then you don’t even need to look at the cards. Eyes closed and some very quick math in your head will look even more magically impressive…
Truth is always obvious to those who know it. And while the truth – or the solution – in this exercise is obvious, it is subtle. Right now, you probably cannot see it. But in a few minutes, it will be difficult not to see it. This is exactly how it occurs for many people when they learn [enter particular skill here] for the first time. You will appear clumsy, and fail often and will want to give up. But once you observe the subtlety of [enter skill,] the difference between being average and very good is obvious…
Reflection Tips & Strategies
Coupled with one or more reflection strategies, here are some sample questions you could use to process your group’s experience after playing this challenging team puzzle:
Did you discover the formula to calculate the birth dates quickly, or slowly?
What did you tell yourself as the activity progressed? Good or bad?
When you finally understood the formula, how did you feel?
The formula in this puzzle is extremely subtle until it becomes very obvious. What elements of your life do you think remain hidden to the group?
The inspiration for Birthday Numbers was sourced from a group of second-grade students in Columbus Ohio (USA.) I was an intern with Project Adventure at the time, and the students took great joy in watching me struggle for a solution that was so obvious to them!