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### Secret Code puzzle 9 june

Secret Code puzzle

A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:

The fifth number plus the third number equals fourteen.

The fourth number is one more than the second number.

The first number is one less than twice the second number.

The second number plus the third number equals ten.

The sum of all five numbers is 30.

What were the five numbers and in what order?

1. 1st - 7
2nd - 4
3rd - 6
4th - 5
5th - 8
--------
Tot - 30
--------

2. 74658
-Tathagata

1. That's wrong it's 74658

2. True. I looked at the answer.

5. 74658,
it was a simple one.

you can do it by trial and error method.. and also deduction..

7. let a = 1st, b = 2nd, c = 3rd, d = 4th, and e = 5th number
"The fifth number plus the third number equals fourteen"
e + c = 14
"The fourth number is one more than the second number"
d = b + 1
"The first number is one less than twice the second number"
a = 2b - 1
"The second number plus the third number equals ten."
b + c = 10
"The sum of all five numbers is 30."
a + b + c + d + e = 30

so we have

e + c = 14
d = b + 1
a = 2b - 1
b + c = 10
a + b + c + d + e = 30

lots of ways to do this
im going to solve for e in the first equation in the form of c,
e + c = 14; e = 14 - c
then im going to solve for c in the 4th equation in terms of b
b + c = 10; c = 10 - b
then im going to rewrite my new 1st equation subbing in 10-b for c
e = 14 -c ---------> e = 14 -(10-b) -----> e = 14 - 10 + b
e = b + 4
so we have everything in the form of b now because
a = 2b - 1
c = 10 - b
d = b + 1
e = b + 4
so now we can sub everthing into the last equation
a + b + c + d + e = 30
(2b -1) + b + (10 - b) + (b + 1) + (b + 4) = 30
4b + 14 = 30
4b = 30 - 14
4b = 16; 4b/4 = 16/4
b = 4
now i can sub 4 in for b in all of those equations and get everything
a = 2b - 1; a = 2(4) -1; a = 8 - 1; a = 7
c = 10 - b; c = 10 - 4; c = 6
d = b + 1; d = 4 + 1; d = 5
e = b + 4; e = 4 + 4; e = 8
a = 7; b = 4; c = 6; d = 5; e = 8

74658

ilovegrace.1210

8. given that x1+x2+x3+x4+x5 = 30 ---->1.
x3+x5=14 ---->2.
that means x1+x2+x4 = 16--->3.
also we have
x4-x2=1 --->4.
2(x2)-x1=1 --->5.
and x2+x3= 10; ---> 6.

on solving 3. and 4 eliminated x4 so now we have a couple of equation in x1 x2,,
which can be solved by a linear system of equation

answer be x1=7 x2=4; x3 =6 ; x4= 5; x5= 8

9. the ans is 74658

10. algebra can do it
let's get some variables we can work with
1st= a
2nd= b
and so on and so forth
so a+b+c+d+e=30
a=2b-1
b+c=10
d=b+1
e+c=14
so this is just a complex system of equations able to be solved by an 8th grader so lets see if a sophomore (i.e. me) can do it: so a is double b - 1 and b is 10 with c added or b one less than d and c is 14 with e added so let's see if e is 1 would it work
1+13 already can't work cause c can't be a 2 digit number
5+9=14 e can be 5 let's keep going
so c is 9+b b is 1 now 9+1=10 c can be 9
now a=2(1)-1 so a is 1 b could be 1
d=b+1 d =2
so with all that plug in to the first equation
1+1+9+2+5=18 wrong so these are not the numbers so we move on to the next number for e (6) and plug it in
6+c=14 c=8
8+b=10 b=2
d=2+1 d=3
a=2(2)-1 a=3
3+2+8+3+6=22 wrong
then e=7
7+c=14 c=7
7+b=10 b=3
d=3+1 d=4
a=2(3)-1 a=5
5+3+7+4+7=26 wrong
and lastly we are at the end of the guess and check
e=8
8+c=14 c=6
6+b=10 b=4
d=4+1 d=5
a=2(4)-1 a=7
7+4+6+5+8=30 correct
a b c d e
so the answer as everyone can clearly see from other posts is 7,4,6,5,8

11. e+c=14
d=b+1
b+c=10
c=10-b
a=2b-1
abcde=30
abd=30-e+c=14
abd=2b-1+b+b+1=16
4b=16
b=4
d = b+1=4+1=5
a = 2b-1 = 8-1=7
c=10-b = 10-4=6
e = 30 - (7+4+6+5) = 8

Ans = 74658

13. b+z = 14
a=y+1
x+1=2y
y+z=10
x+y+z+a+b =30
x+y+a=16
y+1+2y-1 + y =16

y=4
x=7
z=6
b=8
a=5
so the number is 74658

14. 74658 is correct. But so is 55569. Nobody said that numbers can't repeat. And in a key code, they usually can repeat.