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Q.

How many pairs of letters in the word interpretation?

Asked by TARUN MANGLANI, 16 Mar 11:22 pm
4000 characters remaining

1.

I,n,t,e,r (five)
Answered by Francisco, 17 Mar 01:14 am

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2.

Five.
Answered by QueSera Sera, 16 Mar 11:35 pm

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3.

M M',
A A
T T
H E I C S

The permutation
M A T H E M T I A C S
has the pairs
MA AT TH HE EM MT TI IA AC CS
which are all different.

My interpretation of the problem is that it asks

There are eleven ! / two! two! two! total permutations, to account for the repeated letters.

We need to use inclusion/exclusion:

Make AA MM TT "super letters" and the consider one, two, or all three of them being present.

All three paired: eight! = forty thousand, three hundred and twenty

Two or more: three * nine! / two! = five hundred and forty-four thousand, three hundred and twenty
e.g. MM and AA permuted with other nine letters, but the T's can swap without it being different

One or more: three * ten! / two! two! = about two.seven million

Total permutations = eleven! / two! two! two! = about five million

One or more counts the twos extra times,
and two or more counts the threes extra times.

So we have one or more pairs =
t ...more
Answered by Mickey, 16 Mar 11:24 pm

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