# Thread: The Birthday Card Game

1. 0

## The Birthday Card Game

Here are five birthday cards

The 1’s card

1 3 5 7
9 11 13 15
17 19 21 23
25 27 29 31

The 2’s card

2 3 6 7
10 11 14 15
18 19 22 23
26 27 30 31

The 4’s card

4 5 6 7
12 13 14 15
20 21 22 23
28 29 30 31

The 8’s card

8 9 10 11
12 13 14 15
24 25 26 27
28 29 30 31

The 16’s card

16 17 18 19
20 21 22 23
24 25 26 27
28 29 30 31

For each card, if your birthday (day of month only) is on the card, "keep" it. If yor birthday is not on the card, discard it.

Now add up the numbers in the upper left-hand corner of the cards that you kept. That’s your birthday!

2. 0
Worked for me.

3. 0
It worked!

4. 0
Only one card has a 2, so it worked.

5. 0
Wow! This is so cool! It totally worked!

6. 0
Originally Posted by PolymerBob
Only one card has a 2, so it worked.
That is actually a clue to how it works. Note that 1, 4, 8, and 16 also appear on only one card each.

7. 0
Worked for me!

My b-day was on three of the cards. Will more clues follow?

8. 0
Think binary.

9. 0
Originally Posted by Mathman
That is actually a clue to how it works. Note that 1, 4, 8, and 16 also appear on only one card each.
2^1, 2^2, 2^3, 2^4... actually you can do this game with n cards?

10. 0
Originally Posted by seniorita
2^1, 2^2, 2^3, 2^4... actually you can do this game with n cards?
n=4.

On Jupiter, the length of day is about 9.8 Earth hours and the period of revolution of the principal moon (Ganymede) is about 7.15 Earth days. This works out to about 17.5 Jupiter days in each Jupiter month.

The custom on Jupiter is to number the days of the month from 0 to 15, and anyone born on the 16th (full moon) is considered blest and enters into the service of the moon goddess, and is not assigned a birthday.

What numbers should be on each of the four birthday cards for this trick to work on Jupiter, for birthdays 0 up to 15?

11. 0
oh come on, i just got back from work...

Ok i get a pen

12. 0
Voila

The 1’s card

1 3 5 7
9 11 13 15

The 2’s card

2 3 6 7
10 11 14 15

The 4’s card

4 5 6 7
12 13 14 15

The 8’s card

8 9 10 11
12 13 14 15

In Jupiter I dont have birthday, that means no gifts?

n=4
no I meant in general, regardless of the days, you can have as much as cards with power of 2 that dont surpass the overall number (like 31 for earth). Like in my planet for example, month is divided in 63 days

13. 0
And what if your planet has months with an even number of days?

14. 0
i dont think it is a case of even numbers, but not to have the days that are a power of 2. If it was 30 days cards would be like
The 1’s card

1 3 5 7
9 11 13 15
17 19 21 23
25 27 29

The 2’s card

2
3 6 7
10 11 14 15
18 19 22 23
26 27 30

The 4’s card

4
5 6 7
12 13 14 15
20 21 22 23
28 29 30

The 8’s card

8
9 10 11
12 13 14 15
24 25 26 27
28 29 30

The 16’s card

16
17 18 19
20 21 22 23
24 25 26 27
28 29 30

but if it was 32 days=2^5 the next card would have to be something like
32 :sheesh:
I mean I think so, but I m not Mathman!

15. 0
If it was 32, you could could count 32 as 0 and still use the same cards as for 1 up to 31. If your birthday fell on the 32nd, then you would hold no cards, and your birthday comes out as zero.

If you have an odd-ball number of days (not close to a power of two), you could either do what Seniorita did above and fill up the rest of the card with random symbols. Or, you could just write down all the numbers up to the next power of two and it would just turn out than no one has a birthday on some of the days listed on the cards.

For instance, if a month had 100 days you could put all the numbers up to 127 on seven cards. This would do no harm even though no one has birthday number 116, for instance.

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