Bus ticket and sum of digits puzzle

• K Sengupta
In summary: WOW HAHAHA. When I first did it I realized that but when I looked at it AGAIN I guess I forgot. I'm so dumb :tongue:
K Sengupta
Yesterday Professor Q rode on a bus with his friend. As soon as he got the tickets for himself and his friend, which were consecutively numbered with each of the tickets bearing a 5-digit number with no leading zero, he added the digits on them and told his friend that the sum of all ten digits was exactly 62.

His logical friend asked him if the sum of the numbers on either of the tickets was by any chance 35. Professor Q answered his friend, whereby his friend immediately deduced the numbers on the bus tickets.

What were the numbers on the two bus tickets?

56789
56790

I know that if the answer to the question is yes, then the last digit has to be a 9 and the four other digits have to add up to 26, is there any other logic than that?

Last edited:
f(x) wouldn't say 46799 fulfill what is required (for the first ticket as well)... I got the same numbers as you my first try but I assumed numbers don't repeat on individual tickets... but it doesn't say that in the riddle.

Sorry! said:
f(x) wouldn't say 46799 fulfill what is required (for the first ticket as well)... I got the same numbers as you my first try but I assumed numbers don't repeat on individual tickets... but it doesn't say that in the riddle.

But does it add up to 62?

ƒ(x) said:
But does it add up to 62?

Well you need a second ticket... 46799 + 56790 orrr 46790 + 37890 is this wrong and I am crazy or does the first number make 35 and the sum of all 10 makes 62...?
How about
56789 + 37890?

There are so man possible combinations... even that second one none of the numbers repeat on the same ticket but the answer still varies from what you gave...

Sorry! said:
Well you need a second ticket... 46799 + 56790 orrr 46790 + 37890 is this wrong and I am crazy or does the first number make 35 and the sum of all 10 makes 62...?
How about
56789 + 37890?

There are so man possible combinations... even that second one none of the numbers repeat on the same ticket but the answer still varies from what you gave...

But they have to be consecutive digits

ƒ(x) said:
But they have to be consecutive digits

WOW HAHAHA. When I first did it I realized that but when I looked at it AGAIN I guess I forgot. I'm so dumb

If sum of digits of either number is 35, there are many possible answers, but if neither is 35 - there is only one.

98999 & 99000

1. What is the Bus ticket and sum of digits puzzle?

The Bus ticket and sum of digits puzzle is a mathematical game that involves finding the number of ways to create a given sum by adding the digits on a bus ticket. It is also known as the Happy Number puzzle or the Moscow Puzzles.

2. How do you play the Bus ticket and sum of digits puzzle?

To play the Bus ticket and sum of digits puzzle, you must start with a 6-digit bus ticket number. Then, you need to add together all of the digits on the ticket to get a total sum. The goal is to find all possible combinations of digits that add up to the given sum.

3. What is the solution to the Bus ticket and sum of digits puzzle?

The solution to the Bus ticket and sum of digits puzzle is not a single number, but rather a set of all possible 6-digit numbers that have the same sum of digits as the given ticket number. These numbers are known as "Happy Numbers" and have unique properties in mathematics.

4. What is the significance of the Bus ticket and sum of digits puzzle?

The Bus ticket and sum of digits puzzle has been used as a brain teaser and a tool for teaching mathematics. It also has real-world applications in coding and cryptography, as well as being related to the concept of digital roots in number theory.

5. Are there any variations of the Bus ticket and sum of digits puzzle?

Yes, there are several variations of the Bus ticket and sum of digits puzzle, such as using different ticket lengths or finding a specific pattern in the sum of digits. There are also similar puzzles that involve finding the sum of digits for other numbers, such as phone numbers or license plates.

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