Mixing
My Social Security Card Number
Clash Royale CLAN TAG#URR8PPP
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5
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I have forgotten my social security card number. All I remember is that it is the largest integer with the property that the block of any two of its digits that are adjacent is either a two-digit prime number or a two-digit perfect square, and that these are all different.
What is it?
mathematics number-theory arithmetic
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
 |Â
show 1 more comment
up vote
5
down vote
favorite
I have forgotten my social security card number. All I remember is that it is the largest integer with the property that the block of any two of its digits that are adjacent is either a two-digit prime number or a two-digit perfect square, and that these are all different.
What is it?
mathematics number-theory arithmetic
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
2
That's a very interesting thing to remember about your social security card number ...
– Rand al'Thor
3 hours ago
2
Do we know how many digits is the number?
– Rand al'Thor
3 hours ago
1
@Randal'Thor: No, I cannot remember that either. Quite a few...
– Bernardo Recamán Santos
3 hours ago
1
Do the 2-digit blocks overlap? Can a 2-digit number have a leading 0?
– Weather Vane
2 hours ago
2
For no particular reason... What is your mother's maiden name and what was the name of your first/current/favorite pet? :)
– Chowzen
1 hour ago
 |Â
show 1 more comment
up vote
5
down vote
favorite
up vote
5
down vote
favorite
I have forgotten my social security card number. All I remember is that it is the largest integer with the property that the block of any two of its digits that are adjacent is either a two-digit prime number or a two-digit perfect square, and that these are all different.
What is it?
mathematics number-theory arithmetic
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
I have forgotten my social security card number. All I remember is that it is the largest integer with the property that the block of any two of its digits that are adjacent is either a two-digit prime number or a two-digit perfect square, and that these are all different.
What is it?
mathematics number-theory arithmetic
mathematics number-theory arithmetic
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
asked 3 hours ago
Bernardo Recamán Santos
1,8171034
1,8171034
2
That's a very interesting thing to remember about your social security card number ...
– Rand al'Thor
3 hours ago
2
Do we know how many digits is the number?
– Rand al'Thor
3 hours ago
1
@Randal'Thor: No, I cannot remember that either. Quite a few...
– Bernardo Recamán Santos
3 hours ago
1
Do the 2-digit blocks overlap? Can a 2-digit number have a leading 0?
– Weather Vane
2 hours ago
2
For no particular reason... What is your mother's maiden name and what was the name of your first/current/favorite pet? :)
– Chowzen
1 hour ago
 |Â
show 1 more comment
2
That's a very interesting thing to remember about your social security card number ...
– Rand al'Thor
3 hours ago
2
Do we know how many digits is the number?
– Rand al'Thor
3 hours ago
1
@Randal'Thor: No, I cannot remember that either. Quite a few...
– Bernardo Recamán Santos
3 hours ago
1
Do the 2-digit blocks overlap? Can a 2-digit number have a leading 0?
– Weather Vane
2 hours ago
2
For no particular reason... What is your mother's maiden name and what was the name of your first/current/favorite pet? :)
– Chowzen
1 hour ago
2
2
That's a very interesting thing to remember about your social security card number ...
– Rand al'Thor
3 hours ago
That's a very interesting thing to remember about your social security card number ...
– Rand al'Thor
3 hours ago
2
2
Do we know how many digits is the number?
– Rand al'Thor
3 hours ago
Do we know how many digits is the number?
– Rand al'Thor
3 hours ago
1
1
@Randal'Thor: No, I cannot remember that either. Quite a few...
– Bernardo Recamán Santos
3 hours ago
@Randal'Thor: No, I cannot remember that either. Quite a few...
– Bernardo Recamán Santos
3 hours ago
1
1
Do the 2-digit blocks overlap? Can a 2-digit number have a leading 0?
– Weather Vane
2 hours ago
Do the 2-digit blocks overlap? Can a 2-digit number have a leading 0?
– Weather Vane
2 hours ago
2
2
For no particular reason... What is your mother's maiden name and what was the name of your first/current/favorite pet? :)
– Chowzen
1 hour ago
For no particular reason... What is your mother's maiden name and what was the name of your first/current/favorite pet? :)
– Chowzen
1 hour ago
 |Â
show 1 more comment
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
I think the answer is
253797364171613119
Proof:
We cannot use zeros; a two digit number ending in zero is not prime and 00 is the only square, so zeros can only appear at the beginning and can therefore be ignored.
Let's list the squares we can use: 16, 25, 36, 49, 64, 81
and the primes: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
It's a bit like
domino: to maximize the total number, we first need to maximize the number of pairs we can make.
See the following table:
. start end match1 5 6 52 3 0 03 3 6 34 4 1 15 2 1 16 3 2 27 3 5 38 3 0 09 1 6 1
So we can make
16 matches, for a 18 digit Social Security Card Number.
In theory, we want
the largest numbers to appear first, but the only pair ending in 5 is 25.
So we start with 25.
The next one cannot be 59, because we need the 9 for both 79 and 19; one of them can be at the very end
but the other must be somewhere inside the number.
So the next one is 53, then 37, then 79, then 97, then 73, then 36.
67 won't work, as we've used up all our sevens except for the one needed for 17; so we take 64.
We've used up all our nines, sevens and threes except for the one needed for 13; so we take 41.
The next one is 71, then 71, then 16, then 61, then 13, then 31, then 11, and finally 19.
Concatenating all the pairs we get the answer:
253797364171613119
answered 1 hour ago
Glorfindel
11.7k34474
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
I think the answer is
253797364171613119
Proof:
We cannot use zeros; a two digit number ending in zero is not prime and 00 is the only square, so zeros can only appear at the beginning and can therefore be ignored.
Let's list the squares we can use: 16, 25, 36, 49, 64, 81
and the primes: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
It's a bit like
domino: to maximize the total number, we first need to maximize the number of pairs we can make.
See the following table:
. start end match1 5 6 52 3 0 03 3 6 34 4 1 15 2 1 16 3 2 27 3 5 38 3 0 09 1 6 1
So we can make
16 matches, for a 18 digit Social Security Card Number.
In theory, we want
the largest numbers to appear first, but the only pair ending in 5 is 25.
So we start with 25.
The next one cannot be 59, because we need the 9 for both 79 and 19; one of them can be at the very end
but the other must be somewhere inside the number.
So the next one is 53, then 37, then 79, then 97, then 73, then 36.
67 won't work, as we've used up all our sevens except for the one needed for 17; so we take 64.
We've used up all our nines, sevens and threes except for the one needed for 13; so we take 41.
The next one is 71, then 71, then 16, then 61, then 13, then 31, then 11, and finally 19.
Concatenating all the pairs we get the answer:
253797364171613119
answered 1 hour ago
Glorfindel
11.7k34474
add a comment |Â
up vote
3
down vote
accepted
I think the answer is
253797364171613119
Proof:
We cannot use zeros; a two digit number ending in zero is not prime and 00 is the only square, so zeros can only appear at the beginning and can therefore be ignored.
Let's list the squares we can use: 16, 25, 36, 49, 64, 81
and the primes: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
It's a bit like
domino: to maximize the total number, we first need to maximize the number of pairs we can make.
See the following table:
. start end match1 5 6 52 3 0 03 3 6 34 4 1 15 2 1 16 3 2 27 3 5 38 3 0 09 1 6 1
So we can make
16 matches, for a 18 digit Social Security Card Number.
In theory, we want
the largest numbers to appear first, but the only pair ending in 5 is 25.
So we start with 25.
The next one cannot be 59, because we need the 9 for both 79 and 19; one of them can be at the very end
but the other must be somewhere inside the number.
So the next one is 53, then 37, then 79, then 97, then 73, then 36.
67 won't work, as we've used up all our sevens except for the one needed for 17; so we take 64.
We've used up all our nines, sevens and threes except for the one needed for 13; so we take 41.
The next one is 71, then 71, then 16, then 61, then 13, then 31, then 11, and finally 19.
Concatenating all the pairs we get the answer:
253797364171613119
answered 1 hour ago
Glorfindel
11.7k34474
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
I think the answer is
253797364171613119
Proof:
We cannot use zeros; a two digit number ending in zero is not prime and 00 is the only square, so zeros can only appear at the beginning and can therefore be ignored.
Let's list the squares we can use: 16, 25, 36, 49, 64, 81
and the primes: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
It's a bit like
domino: to maximize the total number, we first need to maximize the number of pairs we can make.
See the following table:
. start end match1 5 6 52 3 0 03 3 6 34 4 1 15 2 1 16 3 2 27 3 5 38 3 0 09 1 6 1
So we can make
16 matches, for a 18 digit Social Security Card Number.
In theory, we want
the largest numbers to appear first, but the only pair ending in 5 is 25.
So we start with 25.
The next one cannot be 59, because we need the 9 for both 79 and 19; one of them can be at the very end
but the other must be somewhere inside the number.
So the next one is 53, then 37, then 79, then 97, then 73, then 36.
67 won't work, as we've used up all our sevens except for the one needed for 17; so we take 64.
We've used up all our nines, sevens and threes except for the one needed for 13; so we take 41.
The next one is 71, then 71, then 16, then 61, then 13, then 31, then 11, and finally 19.
Concatenating all the pairs we get the answer:
253797364171613119
answered 1 hour ago
Glorfindel
11.7k34474
I think the answer is
253797364171613119
Proof:
We cannot use zeros; a two digit number ending in zero is not prime and 00 is the only square, so zeros can only appear at the beginning and can therefore be ignored.
Let's list the squares we can use: 16, 25, 36, 49, 64, 81
and the primes: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
It's a bit like
domino: to maximize the total number, we first need to maximize the number of pairs we can make.
See the following table:
. start end match1 5 6 52 3 0 03 3 6 34 4 1 15 2 1 16 3 2 27 3 5 38 3 0 09 1 6 1
So we can make
16 matches, for a 18 digit Social Security Card Number.
In theory, we want
the largest numbers to appear first, but the only pair ending in 5 is 25.
So we start with 25.
The next one cannot be 59, because we need the 9 for both 79 and 19; one of them can be at the very end
but the other must be somewhere inside the number.
So the next one is 53, then 37, then 79, then 97, then 73, then 36.
67 won't work, as we've used up all our sevens except for the one needed for 17; so we take 64.
We've used up all our nines, sevens and threes except for the one needed for 13; so we take 41.
The next one is 71, then 71, then 16, then 61, then 13, then 31, then 11, and finally 19.
Concatenating all the pairs we get the answer:
253797364171613119
answered 1 hour ago
Glorfindel
11.7k34474
edited 1 hour ago
answered 1 hour ago
Glorfindel
11.7k34474
answered 1 hour ago
Glorfindel
11.7k34474
answered 1 hour ago
Glorfindel
11.7k34474
11.7k34474
add a comment |Â
add a comment |Â
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2
That's a very interesting thing to remember about your social security card number ...
– Rand al'Thor
3 hours ago
2
Do we know how many digits is the number?
– Rand al'Thor
3 hours ago
1
@Randal'Thor: No, I cannot remember that either. Quite a few...
– Bernardo Recamán Santos
3 hours ago
1
Do the 2-digit blocks overlap? Can a 2-digit number have a leading 0?
– Weather Vane
2 hours ago
2
For no particular reason... What is your mother's maiden name and what was the name of your first/current/favorite pet? :)
– Chowzen
1 hour ago