Mensa Calendar Error (aka Z-man has trouble with addition vs. multiplication)
 

So - so today's puzzle reads:

I came up with two possible solutions, but the Mensa answer says there is only one.

Can you find the answer?

-Z

628549

scratch the second one

That's the only answer I see, what else did you come up with?

Is this in base 10?

642537
or
624537 if they mean the 4th digit must come before the 5th in the product sequence.

First digit must be four more than second

738169

But I thought the fourth and fifth digits when read as a single number equal the product of the first and sixth digits. The product of 7 and 9 is not 16.

"the fourth and fifth digits when read as a single number equal the product of the first and sixth digits"

You're adding, "product" means multiply.

to translate the puzzle into something more easily readable.

variables A,B,C,D,E in integer space {1,2,3,4,5,6,7,8,9}
variable F in integer space {1,3,5,7,9}

where A<>B<>C<>D<>E<>F (non repeated digits)
A=B+4
C=F-1
D*10+E=A*F



solving....

A=B+4 would limit A to {5,6,7,8,9} and B to {1,2,3,4}
C=F-1 would limit C to {2,4,6,8} and F to {3,5,7,9}

E is basically free to be any digit.
E=A*F-D*10

i think 952637 works

I was assuming the 1st digit was in the 10^0 place, 2nd digit was in the 10^1 place etc.

What do you mean with "2 numbers , read as a single digit" ????

"when read as a single number " 12, for example.

ahh true there's an ambiguity i assumed first digit is 10^5 place.

ok, now i get it
well, what island said : 628549 seems right to me

Third digit is not one less than the sixth

oh heh. yea i did 5th.

the real thing is. not only do u have to find 1 case. u have to then prove that there's none other than 1 case proving it....i need to do more formal math....and i'm out of brain cells now

Yep. Oppsy. Never could get my addition and mutiplication straight! :eek:

I guess you have to like math to want to join Mensa. I could do geometry, physics, and aerodynamics but this stuff is not my cup of anything.

IMHO this isn't really a "brain teaser" or even a puzzle of any kind: it's too easy to brute-force in any programming language you may choose to utilize.

288!!

Wait! Or is it 2?

;)

I lol'd again. :D

416287

418369

8675301 Call Jenny.

The 2nd digit has to be 4 less then the 1st digit

The 2nd digit has to be 4 less then the 1st digit
The 3rd has to be 1 less then the 6th

you're getting worse with each try !

Oh crap!
By "4 more" I was multiplying!
Back to grade school math. :D

+1

I couldnt find another one.

Not really , 3rd digit must b 1 less then the 6th..
your third digit is 5 less then the 6th

Rule 1
6 digits

Rule 2
odd number

Rule 3
No zeroes

Rule 4
no repeating digits

rule 5
1st digit = 2nd digit +5

Rule 6
3rd digit = 6th digit -1

rule 7
4th-5th= 1st + 6th








1
So taking into account #1 en #2 #3 and #4

the numbers start at 123457


2
Add Rule 5 and it goes up

512347

Anything lower is not possible, because 5 anything lower then 5 can't be on the 1st digit or it would violate rule #5

First 2 digits can only be

51
62
73
84
95

Nothing else is allowed. with rule 5

3
Rule 6

Third digit, must be even, because it's the 6th digit -1, and the 6th digit must be odd(rule #2)
IT also can't be 0 so the last digit cannot be 1

So third one is either 2 4 6 or 8


XX X
51 2
62 4
73 6
84 8
95

4
LAst digit can only be or 3 5 7 9 ,anything else violates rule #2,#3 or #6


XX X xx x
51 2 3
62 4 5
73 8 9
84 6 7
95


5

Start adding up the possible digit 1's with the possible digit 6 to find the possible digits 4 and 5
5+3 = 8 (rule 7 violation, must have 2 digits)
5+5 (rule #4violation)
5+7 = 12
5+9 = 14

6+3 = 9 (rule 7 violation, must have 2 digits)
6+5 = 11 (rule 4 repeating digits)
6+7 = 13
6+9 = 15

7+3 = 10 (rule 3 no zeroes)
7+5 = 12
7+7 (rule #4violation)
7+9 = 15

8+3 = 11
8+5 = 13
8+7 = 15
8+9 = 17


9+3 = 12
9+5 = 14
9+7 = 16
9+9(rule #4violation)


So that leaves only these possibilities for the 4th and 5th digit
11
12
13
14
15
16
17

So this also means #1 is ruled out of all the other digits


XX X xx x
95 2 1 3
62 4 5
73 8 9
84 6 7


6
remaining combinations are

842125
842157
842179
846125
846157
846179
732169
734125
734169
738125
738169
736169
736125
624137
624159
628137
628159
952167
954167
958167

No calculator , or brute force programming used.
Haven't checked all the results yet...

CHIT

4th and 5th are the multiplication of 1st and 6th

CRAP

corrected


Rule 1
6 digits

Rule 2
odd number

Rule 3
No zeroes

Rule 4
no repeating digits

rule 5
1st digit = 2nd digit +4

Rule 6
3rd digit = 6th digit -1

rule 7
4th-5th= 1st + 6th








1
So taking into account #1 en #2 #3 and #4

the numbers start at 123457


2
Add Rule 5 and it goes up

512347

Anything lower is not possible, because 5 anything lower then 5 can't be on the 1st digit or it would violate rule #5

First 2 digits can only be

51
62
73
84
95

Nothing else is allowed. with rule 5

3
Rule 6

Third digit, must be even, because it's the 6th digit -1, and the 6th digit must be odd(rule #2)
IT also can't be 0 so the last digit cannot be 1

So third one is either 2 4 6 or 8


XX X
51 2
62 4
73 6
84 8
95

4
LAst digit can only be or 3 5 7 9 ,anything else violates rule #2,#3 or #6


XX X xx x
51 2 3
62 4 5
73 8 9
84 6 7
95


5

Start multiplying the possible digit 1's with the possible digit 6 to find the possible digits 4 and 5
5x3 = 15 (rule #4violation)
5x5 (rule #4violation)
5x7 = 35 (rule #4violation)
5x9 = 45(rule #4violation)

6x3 = 18
6x5 = 30 (Rule3)
6x7 = 42 (rule #4violation)
6x9 = 54

7x3 = 21
7x5 = 35 (rule #4violation)
7x7 (rule #4violation)
7x9 = 63 (rule #4violation)

8x3 = 24 (rule #4violation)
8x5 = 40 (rule #3)
8x7 = 56
8x9 = 72


9x3 = 27
9x5 = 45(rule #4violation)
9x7 = 63
9x9 (rule #4violation)


So that leaves only these possibilities for the 4th and 5th digit

62x183
62x549

84x567
84x729

95x273
95x637

apply rule 6 (3rd = 6th -1)

622183 (rule #4violation)
628549
846567 (rule #4violation)
848729 (rule #4violation)
952273(rule #4violation)
956637 (rule #4violation)



That leaves only 1

628549

rule le 1
6 digits CHECK

Rule 2
odd number CHECK

Rule 3
No zeroes CHECK

Rule 4
no repeating digits CHECK

rule 5
1st digit = 2nd digit +4 CHECK

Rule 6
3rd digit = 6th digit -1 CHECK

rule 7
4th-5th= 1st + 6th CHECK

Isn't MENSA famous for being full of dip schits? I've heard a lot of funny jokes about it.

Dunno, i'm to stupid to join.

8675309

Good explanation Stijn.

troll.