Math Is Fun Forum

gheharuko176

Banned

Registered: 2021-10-29

Posts: 1

Puzzles and Games » Addition Problem

Given the digits 1,2,3,4,5,6 & 7, how can we construct an addition problem whose sum is 100? You may use each digit only once.

Last edited by zetafunc (2022-05-05 19:48:51)

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,893

Re: Puzzles and Games » Addition Problem

Hi gheharuko176, and welcome to the Forum!

Given the digits 1,2,3,4,5,6 & 7, how can we construct an addition problem whose sum is 100? You may use each digit only once.

 56
 13
 24
  7
---
100
===

Last edited by phrontister (2022-05-04 22:59:23)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Puzzles and Games » Addition Problem

hi gheharuko176

Welcome to the forum.

Looks like there are multiple solutions.  I had 67 + 23 + 1 + 4 + 5

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,893

Re: Puzzles and Games » Addition Problem

Hi Bob;

Looks like there are multiple solutions.

I found the following solution ranges (in ascending 7-digit permutation order):
  (a) 720 solutions for sums of 3 single-digit numbers and 2 double-digit numbers, ranging from 1+2+4+36+57=100 to 7+6+4+52+31=100
  (b) 288 solutions for sums of 1 single-digit number and 3 double-digit numbers, ranging from 2+15+36+47=100 to 7+56+24+13=100

Last edited by phrontister (2021-10-31 02:08:37)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Puzzles and Games » Addition Problem

hi Phro,

Neat! That would explain why I managed to come up with a solution so quickly. 

Keep crunching!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,893

Re: Puzzles and Games » Addition Problem

That would explain why I managed to come up with a solution so quickly. 

Same here! With mine, I thought, "That was waaay too quick!!".

So...curiosity got the better of me, and I explored further via the list of permutations from MIF's Permutations Calculator & some operations on them in Excel.

Last edited by phrontister (2021-11-01 09:29:40)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

CurlyBracket

Member

From: Your Maths Textbook

Registered: 2022-01-03

Posts: 155

Re: Puzzles and Games » Addition Problem

Umm... Pardon me,  but isn't this thread an advertisement about a massaging chair?

---

Filling the unforgiving minute with sixty seconds’ worth of distance run!

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,893

Re: Puzzles and Games » Addition Problem

Well, yes...it is now, but it began 30/10/2021 as an apparently genuine maths 'problem' (see post #2, which I edited to include the original 'problem' that the OP since replaced with the chair ad, possibly on 26/11/2021).

I said 'problem', because the level of simplicity of the OP's 'problem' raises the suspicion that the post was a bogus springboard to be used later, as it now seems to have been, for placing the ad via an edit to the original post.

A moderator should look at this...

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Puzzles and Games » Addition Problem

Thanks both -- I've edited the original post back to what it was (and it should stay that way).