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Step 1)
Notice that the difference of 2 four digit number is a three digit number,
this implies that (look at thousand column) a - c = 0 or a - c - 1 = 0
(in the case of hundred column borrowing from thousands column).

If a - c = 0, then (look at ones column) e = 0
and implies that the subtraction result is a two digit number which is not true.
Therefore, a - c - 1 = 0 -> a = c + 1.

Step 2)
Notice that (look at ones column) a - c = e or 10 + a - c = e
(in the case of hundred column borrowing from tens column).

Substitute a from step 1.
If 10 + a - c = e, then 10 + a - c = e -> 10 + c + 1 - c = e -> e = 11
However, c is a one digit, so this assumption must be false.
Therefore, a - c = e -> c + 1 - c = e -> e = 1
a b b a
c d d c
_______-
1 f 1

Step 3)
Notice that a = c + 1, however, (look at thousands column) the result is three digit,
this implies that b < d and borrow from the thousands column , 10 + b - d = 1 or 10 + b - d - 1 = 1

If 10 + b - d = 1, this implies that the tens column doesn't borrow, however, b < d,
so this assumption must be false.
Therefore, 10 + b - d - 1 = 1 -> 8 + b = d -> b = 0, d = 8 or b = 1, d = 9
Otherwise, d is a two digit number

Step 4)
Notice that, since a = c + 1 the ones column doesn't borrow from the tens column and b < d,
therefore 10 + b - d = f (in the case of hundred column borrowing from tens column).

Substitute b and d from step 3.
Case 1 : b = 0, d = 8
10 + 0 - 8 = f -> f = 2
Case 2 : b = 1, d = 9
10 + 1 - 9 = f -> f = 2
In either case, f = 2
a b b a
c d d c
_______-
1 2 1

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

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Remember to wrap math in`\(`

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`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestYou have until next Saturday, $3:00$pm!

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Rewrite as

Step 1) Notice that the difference of 2 four digit number is a three digit number, this implies that (look at thousand column) a - c = 0 or a - c - 1 = 0 (in the case of hundred column borrowing from thousands column).

Step 2) Notice that (look at ones column) a - c = e or 10 + a - c = e (in the case of hundred column borrowing from tens column).

Step 3) Notice that a = c + 1, however, (look at thousands column) the result is three digit, this implies that b < d and borrow from the thousands column , 10 + b - d = 1 or 10 + b - d - 1 = 1

Step 4) Notice that, since a = c + 1 the ones column doesn't borrow from the tens column and b < d, therefore 10 + b - d = f (in the case of hundred column borrowing from tens column).

Therefore, C = 121

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That's wrong. Try again!

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I see, I forgot the carrier. BTW, do you do integral?

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