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Two eggs brainteaser

By David, 14 October 2020 Brainteaser

Difficulty: Taxing

Jenny found a strange sum written on a piece of paper:
EGG + EGG = PAGE

Each letter represents a different digit, so P might be 1, for example. Can you work out what the sum really is?

Scroll down or click for a hint, or the answer!

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Brainteaser hint 1

Writing it upright might make this easier:

 EGG
+EGG
PAGE

Look at the ones column and the tens column. Do you see a difference? This could narrow down your options to solve the problem by using algebra, or trial and error.

Brainteaser hint 2

If you look at just the ones column and the tens column, you’ll see:
GG + GG = GE
Adding GGs together gives two different letters. There must be a 1 being carried!

Brainteaser hint 3

Still stuck? If carrying a 1, G must be one of these options: 5, 6, 7, 8 or 9.
What answers do you get if you calculate each of these options for GG + GG? What options does that leave for E?

 

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Brainteaser answer

If you look at the last two digits of each number, you’ll see:
GG + GG = GE
As mentioned in the hints, there must be a 1 being carried!

Looking at just the tens column:
G + G + 1 = 10 + G
G + G = 9 + G
So, G = 9

Then looking at the ones column:
G + G = 10 + E
9 + 9 = 10 + E
So, E = 8

The final sum is:
899 + 899 = 1798
This reveals the final letters:
P = 1 and A = 7

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