# Where to put 1,2,3,4,5,6,7,8?

In the picture below? Once each i guess. I think it's a trick and is not necessarily something that adds up to 9 on the left column. Idk. Haha.

Any hints please?

## 2 Answers

[EDIT]
Possible strategy other than brute force.
This is not possible with 100% logical deduction so you will have to make assumptions at one point.
Let's transform this first into an addition because it's easier to explain.
So the equation above translates to

ABC + DEF = 9GH.

pick 2 digits (A & D) that add up to 9.
The position is not important because in addition they are obviously interchangeable.
Let's pick 1 & 8, the obvious case.

Now you have 1BC+8EF=9GH.
Since there is no carry over we can reduce this to BC+EF = GH. and the available digits 2,3,4,5,6,7.
Then try to split them in 2 groups so that 2 digits from the group add up to the third one. This is the simple case, without carry over.
I wasn't able to find such groups.
You can try to find a combination with a carry over.
Then move to the second case. Pick 7 and 2. And then 6 & 3.

After you are done with this, you can consider the case with a carry over from the tenths position. So, as you said, pick 2 numbers that add up to 8. Then move to the equation BC+EF = GH with the remaining digits. [/EDIT]

Here is the brute force approach.
I wrote some PHP code. Ignore the way it looks. It was done fast with stackoverflow help for permutations.

<?php

function pc_permute($items,$perms = array( )) {
if (empty($items)) {$return = array($perms); } else {$return = array();
for ($i = count($items) - 1; $i >= 0; --$i) {
$newitems =$items;
$newperms =$perms;
list($foo) = array_splice($newitems, $i, 1); array_unshift($newperms, $foo);$return = array_merge($return, pc_permute($newitems, $newperms)); } } return$return;
}
$array = array(1, 2, 3, 4, 5, 6, 7, 8);$permutations = pc_permute($array); foreach ($permutations as $p) {$one = (int)('9'.$p[0].$p[1]);
$two = (int)($p[2].$p[3].$p[4]);
$diff = (int)($p[5].$p[6].$p[7]);
if ($one -$two == $diff) { echo '&nbsp;'.$one.'<br />-'.$two.'<br />----<br />='.$diff.'<br /><br />';
}
}
?>


This prints out 96 combinations.

 972
-314
----
=658

972
-614
----
=358

963
-215
----
=748

963
-715
----
=248

954
-216
----
=738

954
-716
----
=238

945
-317
----
=628

945
-617
----
=328

954
-236
----
=718

963
-245
----
=718

945
-327
----
=618

972
-354
----
=618

945
-627
----
=318

972
-654
----
=318

954
-736
----
=218

963
-745
----
=218

981
-324
----
=657

981
-624
----
=357

945
-318
----
=627

981
-354
----
=627

945
-618
----
=327

981
-654
----
=327

945
-328
----
=617

945
-628
----
=317

927
-341
----
=586

927
-541
----
=386

918
-342
----
=576

918
-542
----
=376

981
-235
----
=746

918
-372
----
=546

927
-381
----
=546

918
-572
----
=346

927
-581
----
=346

981
-735
----
=246

954
-218
----
=736

981
-245
----
=736

954
-718
----
=236

981
-745
----
=236

954
-238
----
=716

954
-738
----
=216

918
-243
----
=675

918
-643
----
=275

963
-218
----
=745

981
-236
----
=745

918
-273
----
=645

963
-718
----
=245

981
-736
----
=245

918
-673
----
=245

981
-246
----
=735

981
-746
----
=235

963
-248
----
=715

963
-748
----
=215

936
-152
----
=784

936
-752
----
=184

936
-182
----
=754

972
-318
----
=654

981
-327
----
=654

972
-618
----
=354

981
-627
----
=354

936
-782
----
=154

981
-357
----
=624

981
-657
----
=324

972
-358
----
=614

972
-658
----
=314

945
-162
----
=783

954
-271
----
=683

954
-671
----
=283

945
-762
----
=183

918
-245
----
=673

954
-281
----
=673

918
-645
----
=273

954
-681
----
=273

945
-182
----
=763

945
-782
----
=163

918
-275
----
=643

918
-675
----
=243

936
-154
----
=782

945
-163
----
=782

936
-754
----
=182

945
-763
----
=182

918
-346
----
=572

918
-546
----
=372

945
-183
----
=762

945
-783
----
=162

936
-184
----
=752

936
-784
----
=152

918
-376
----
=542

918
-576
----
=342

954
-273
----
=681

927
-346
----
=581

927
-546
----
=381

954
-673
----
=281

954
-283
----
=671

954
-683
----
=271

927
-386
----
=541

927
-586
----
=341

• Any suggestions on how to come up with an answer 1. by hand 2. other than brute force? What do you think of my suggestion? – BCLC Apr 11 '17 at 12:37
• I've edited the answer with suggestions on where to start. – Marius Apr 11 '17 at 12:52

It's

936-152=784

Any alternatives? Lazy to use excel/Google sheets. Not necessarily teaching logic anyhoo. If ever, we don't know if it's some hindsight bias or something idk.

How i got my answer:

Pick some pair that

adds up to 8

and not

9.

Let's say

1 and 7.

(The above pair has the properties described in hidden text prior)

If we're going to

borrow

then box (1,2) must be

smaller than box (2,2). If they respectively are 3 and 5 then box (3,2) is 8; If 2 and 5, then 7

which is not allowed and so on. Luckily the first pair works.

• Welcome to the site. Firstly, you're not really supposed to answer your own puzzles, especially five minutes after you post them. Secondly, you should put your answer in a spoiler tag in case anyone else wants to try solving it themselves. – F1Krazy Apr 11 '17 at 9:10