Bus ticket and sum of digits puzzle

Click For Summary

Discussion Overview

The discussion revolves around a puzzle involving two consecutively numbered bus tickets, each with a 5-digit number. Participants explore the conditions that the sum of all ten digits equals 62 and whether the sum of the digits on either ticket can equal 35. The focus is on reasoning through possible combinations and constraints of the ticket numbers.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Professor Q's tickets have 5-digit numbers, and the total sum of all ten digits is stated to be 62.
  • Some participants suggest that the sum of the digits on either ticket could be 35, leading to various combinations of ticket numbers.
  • There is uncertainty about whether digits can repeat within individual tickets, as some participants assumed they could not.
  • Multiple combinations are proposed, such as 46799 and 56790, but participants question if these fulfill the conditions of the puzzle.
  • One participant notes that if neither ticket's digits sum to 35, there may only be one valid solution.

Areas of Agreement / Disagreement

Participants express differing views on the validity of certain ticket combinations and the implications of the sum conditions. There is no consensus on the specific numbers of the tickets, and the discussion remains unresolved regarding the correct combinations.

Contextual Notes

Participants highlight the importance of the tickets being consecutively numbered and the implications of digit repetition, which remain unclear. The discussion reflects various assumptions and interpretations of the puzzle's conditions.

K Sengupta
Messages
113
Reaction score
0
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?
 
Mathematics news on Phys.org
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 :wink:
 
ƒ(x) said:
But they have to be consecutive digits :wink:

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 :-p
 
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
 

Similar threads

MHB Crack the Code: A Puzzle Challenge!
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Lorentz Transformation: Premises + Derivation
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Solve Weedy Willie's Division Puzzle
  • · Replies 1 ·
Replies
1
Views
5K
Undergrad Micromass' big October challenge
  • · Replies 125 ·
5
Replies
125
Views
20K
Word Problems In Algebra Help Me Please
  • · Replies 13 ·
Replies
13
Views
5K
A very complicated puzzle: the planet of lies
  • · Replies 2 ·
Replies
2
Views
4K
PF Fan Fiction: Mathematicians in Love
  • · Replies 2 ·
Replies
2
Views
4K
Challenge Math Challenge - December 2018
  • · Replies 67 ·
3
Replies
67
Views
16K
News New Twist on Obama Unemployment Prediction
  • · Replies 34 ·
2
Replies
34
Views
8K
Using physics to prove my innocence
  • · Replies 1 ·
Replies
1
Views
2K