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Neha and Hope Answer: Firstly, we just want to say that this is crazy and HOW does ET know all of this about her phone # but not the actual number?! AND she can just walk instead of wasting her time and money on this
We used guess and check along with the rule that the numbers are not the same in a row and the numbers on the keypad have to touch. Anything that ends in 5 or 0 is automatically ruled out since it can be divided by 5. Anything that ends in an even number as well since it can be divided by 2.
Using these rules, the only possible combinations could be, 987, 957, 907, 963, 953, and 951. 907 works, therefore the last two digits are 0 and 7
next numbers could be 8 5 6 or 0 but if it is six then it has to be three (because 2 is already there) which is divisible by 3 so it has to be 0 and then it can only be seven. so the last digits are 0 and 7.
(212)548-09_ _ The last number cannot be even (otherwise it will be able to be divisible by 2), it cannot be 3,6, or 9 (otherwise it would be divisible by 3), and it cannot be 0 or 5 (otherwise it would be divisible by 5. The last known number of her phone number is 9 and on the keypad, it touches 6,8,5, and 0. The last two digits may be... 87 07 51 57 This is exactly 4 possibilities, unless I calculated it wrong. ET will be able to phone home. Now the real problem is, does she have any quarters?
(212)548-09_ _ The last number cannot be even (otherwise it will be able to be divisible by 2) and it cannot be 0 or 5 (otherwise it would be divisible by 5. The last known number of her phone number is 9 and on the keypad, it touches 6,8,5, and 0. The last two digits may be... 07 59 89 Unless I am wrong, there are 3 possibilities. ET should be able to phone home for a ride. Or she could phone a random number and ask them to find her home phone number in their phone book.
After looking at the clues, the last one gives the biggest hint. First we know that the last digit must be an odd number and can't be 5 or 0 so the only possibilities are 3, 7 or 9. Next, we know that each number in her phone number somehow touches the other. If the 3rd last digit is 9, than the 2nd last digit could be 5,6, 8 or 0. If the second last digit was 5, the last digit could be 1, 3, 7 and 9 because the other numbers are even which isn't applicable. 957 and 951 wouldn't work as they are multiples of 3 but 953 and 959 are possibilities. If the second last digit was 0, then the last digit could be 9 or 7 but 909 wouldn't work as it is a multiple of 3. 907 is another possibility. If the second last digit was 8, then only 9 and 7 could be the last digit. Again, 987 wouldn't work as it is a multiple of 3 but 989 is a possibility. Finally, if 6 was the second last digit, then the possibilities would be 9 and 3 but 963 and 969 are both multiples of 3 so these wouldn't work. In the end, if Esther does the math right, she should be able to get back home as the two last digits could be: 53, 59, 07 and 89. Since she has enough money for 4 phone calls, she is guaranteed to get one right.
The next number must touch 9 so it can be 6, 5, 8, 0 or #. Then, if it is 6, the 3rd number can be 9, 8, 5, 2, or 3. If it is 0 the 3rd can be 7, 8, 9. If 8, the 3rd will be 9, 0, 7, 4, 5, 6. If it is 5, the 3rd number will be any number other than 0.
Now all the combos for the last 3 numbers: 963, 962, 965, 968, 969 951, 952, 953, 954, 956, 957, 958, 959 987, 986, 985, 984, 989, 980 909, 908, 907
Numbers not divisible by 2, 3 or 5 953, 959, 989, 907
There are only 4 possible numbers. Extraterrestrial can call 4 times meaning she should be able to call her home, unless she misclicks and gets unlucky, then she is stuck at a phone booth forever. Or if she is extremely socially awkward and can’t talk to people other than close ones she’s stuck there as well (If she starves at a phone booth, it’s her fault for texting all day and wasting battery, not knowing the phone number and not telling anyone she needed a ride home).
I will solve this using the process of elimination.
First, I write all the possibilities of the numbers that she does not know that do not include two adjacent numbers that are the same and touch each other in the keypad.
Good job to most. I liked seeing your thought process and methodology jotted down. The 4 possible numbers were: (212) 548 - 0953 or (212) 548 - 0959 or (212) 548 - 0989 or (212) 548 - 0907
Ones place: Not 0, 5, 2, 4, 6, 8. Could be 1, 3, 7, 9
ReplyDeleteTens: 0, 8, 5, 6
Last # of Phone# can be: 901, 907, 983, 989, 953, 959, 961, 967
Leo I think you overlooked the fact the the number must be touching in some way on the dial pad.
DeleteYou mean Leon right?
DeleteEdit:
DeleteLast 3 digits: 907, 989, 953, 959,
Neha and Hope Answer:
ReplyDeleteFirstly, we just want to say that this is crazy and HOW does ET know all of this about her phone # but not the actual number?! AND she can just walk instead of wasting her time and money on this
We used guess and check along with the rule that the numbers are not the same in a row and the numbers on the keypad have to touch.
Anything that ends in 5 or 0 is automatically ruled out since it can be divided by 5.
Anything that ends in an even number as well since it can be divided by 2.
Using these rules, the only possible combinations could be, 987, 957, 907, 963, 953, and 951.
907 works, therefore the last two digits are 0 and 7
next numbers could be 8 5 6 or 0 but if it is six then it has to be three (because 2 is already there) which is divisible by 3 so it has to be 0 and then it can only be seven. so the last digits are 0 and 7.
ReplyDelete(212)548-09_ _
ReplyDeleteThe last number cannot be even (otherwise it will be able to be divisible by 2), it cannot be 3,6, or 9 (otherwise it would be divisible by 3), and it cannot be 0 or 5 (otherwise it would be divisible by 5.
The last known number of her phone number is 9 and on the keypad, it touches 6,8,5, and 0. The last two digits may be...
87
07
51
57
This is exactly 4 possibilities, unless I calculated it wrong. ET will be able to phone home. Now the real problem is, does she have any quarters?
oh wait mr.milette please do not post my first answer, it is incorrect. I will send you another one.
ReplyDelete(212)548-09_ _
ReplyDeleteThe last number cannot be even (otherwise it will be able to be divisible by 2) and it cannot be 0 or 5 (otherwise it would be divisible by 5.
The last known number of her phone number is 9 and on the keypad, it touches 6,8,5, and 0. The last two digits may be...
07
59
89
Unless I am wrong, there are 3 possibilities. ET should be able to phone home for a ride. Or she could phone a random number and ask them to find her home phone number in their phone book.
After looking at the clues, the last one gives the biggest hint. First we know that the last digit must be an odd number and can't be 5 or 0 so the only possibilities are 3, 7 or 9. Next, we know that each number in her phone number somehow touches the other. If the 3rd last digit is 9, than the 2nd last digit could be 5,6, 8 or 0. If the second last digit was 5, the last digit could be 1, 3, 7 and 9 because the other numbers are even which isn't applicable. 957 and 951 wouldn't work as they are multiples of 3 but 953 and 959 are possibilities. If the second last digit was 0, then the last digit could be 9 or 7 but 909 wouldn't work as it is a multiple of 3. 907 is another possibility. If the second last digit was 8, then only 9 and 7 could be the last digit. Again, 987 wouldn't work as it is a multiple of 3 but 989 is a possibility. Finally, if 6 was the second last digit, then the possibilities would be 9 and 3 but 963 and 969 are both multiples of 3 so these wouldn't work. In the end, if Esther does the math right, she should be able to get back home as the two last digits could be:
ReplyDelete53,
59,
07 and
89.
Since she has enough money for 4 phone calls, she is guaranteed to get one right.
The next number must touch 9 so it can be 6, 5, 8, 0 or #. Then, if it is 6, the 3rd number can be 9, 8, 5, 2, or 3. If it is 0 the 3rd can be 7, 8, 9. If 8, the 3rd will be 9, 0, 7, 4, 5, 6. If it is 5, the 3rd number will be any number other than 0.
ReplyDeleteNow all the combos for the last 3 numbers:
963, 962, 965, 968, 969
951, 952, 953, 954, 956, 957, 958, 959
987, 986, 985, 984, 989, 980
909, 908, 907
Numbers not divisible by 2, 3 or 5
953, 959, 989, 907
There are only 4 possible numbers. Extraterrestrial can call 4 times meaning she should be able to call her home, unless she misclicks and gets unlucky, then she is stuck at a phone booth forever. Or if she is extremely socially awkward and can’t talk to people other than close ones she’s stuck there as well (If she starves at a phone booth, it’s her fault for texting all day and wasting battery, not knowing the phone number and not telling anyone she needed a ride home).
Facepalm
DeleteI will solve this using the process of elimination.
ReplyDeleteFirst, I write all the possibilities of the numbers that she does not know that do not include two adjacent numbers that are the same and touch each other in the keypad.
09, 08, 07
89, 80, 87, 84, 85, 86
51, 52, 53, 54, 56, 57, 58, 59
63, 69, 62, 65, 68
Next, I will elimate the numbers that in the final three numbers of her phone number that are divisible by 2, 3, or 5.
07, 87, 51, 57 are the only remaining numbers.
Therefore, there are four possibilities and she can call home with her money.
Good job to most. I liked seeing your thought process and methodology jotted down. The 4 possible numbers were: (212) 548 - 0953 or (212) 548 - 0959 or (212) 548 - 0989 or (212) 548 - 0907
ReplyDelete