There is a very hard, very hard…

It’s an Enigma Puzzle.

Enigma #41 is:

(Now, before I do anything, I can’t take credit for ANY OF THE IMAGES AND THINGS, SO CREDIT GOES TO Enigmatic Codes)

To write out the full division.

Look hard?

It was. But if you think carefully enough, it’s pretty straightforward.

Now, how did I solve this?

The first thing you should do in the division substitution is always look at the multiples of the divisor. The distinct multiples of the divisor are:

• rd
• vxv
• vy
• da
• tts

If we knew the divisor, this could have been easier, but we don’t so chart time!

ODD	EVEN
r	s
x	d
t	v
y	m
	a

How do we know that the stated numbers are even and odd? Look at the division working out, and you’ll see that ss – rd = d. That means s is even, because whatever d is, s will be double that, even. and since the difference between ss and rd is one digit, r is one less than s, which is even, so odd. Same deal with tvv and tts, where the difference is s. v is even, and since t is one less than v, it is odd.

Now, if we know that r is odd and v is even, then r – v must be odd. So x is odd. t – x = d, and they are both odd, so even.

See that m – a = x? That means m and a are of the same parity, and y would be the opposite parity. But look at ym – da = x. Since the difference is one digit, and d is even, y must be odd, and hence m and a are even.

How could I use this information to solve the enigma? Look at the unit number. d, v, y, a, s, so that means the divisor is clearly odd. It can’t be too high of a number, since there are three multiples of the divisor lower than 100.

Look at the last subtraction, tvv – tts = s. Here are the possibilities:

s	t
6	1
7	3
8	5
9	7

Remember: s is even, so it brings it down to two solutions: s = 6 and t = 1, or s = 8 and t = 5. That means v = 2 or v = 6, respectively. Therefore, x = 3 or x = 7, also respectively. But let’s look up.

ss – rd.

If s = 6, then ss – rd = 66 – 58. If s = 8, then ss – rd = 88 – 79. But d is even, so s must be 6. So rd is 58.

Remember how the divisor was odd? That means it has to be 29. Its multiples are 29, 58, 87, 116, 145, 174, 203, 232 and 261. So vxv is 232, and tts is 116. So:

• t = 1
• v = 2
• x = 3
• r = 5
• s = 6
• d = 8

Only m, y and a to go.

The missing numbers are 0, 4, 7 and 9. y and a are 7 and 9, not necessarily in that order. xm – vy = t.

3m – 2y = 1. That has to mean that y = 9, m = 0 and a = 7.

So the final answer is: 661580022 ÷ 29 = 22813104 r 6.

Simples.

That reminds me of that Australian ad I saw, and it is not funny.

Okay, me out.

Also, original page: here.