Math Is Fun Forum

Think....Think........Think................

Happiness comes through doors you
didn't even know you left open.

Birthdays are good for you;
the more you have,
the longer you live.

Ever notice that the people who are late
are often much jollier
than the people who have to wait for them?

If shops are lowering prices every day,
how come nothing is free yet?

You may be only one person in the world,
but you may also be the world to one person.

Don't cry because it's over;
Smile because it happened.

Take your time. I am in no hurry.
After you have done it, I'd have to work an hour a day
to add just one or two digits, since that would require checking for all numbers from 0 to 9.
Thank you once again, Administrator.

Well done, Mr T; Keep up the good work!

The three values of the sides of a right angled triangle are also called a Pythagorean Triple.
A Pythagorean triple is a set of three whole numbers , such that one number squared added to another number squared equals the third number squared. Euclid could prove that there are an infinite number of such Pythagorean triples.

Euclid's proof begins with the observation that the difference between successive square numbers is always an odd number.
4 - 1 = 3,  9 - 4 = 5,  16 - 9 = 7, 25 - 16 = 9, 36 - 25 = 11, 49 - 36 = 13 etc.

Mathsy is right! This is a puzzle and crept into 'Help me' by mistake.
Anyway, I shall give the solution.
One dice is marked 0,1,2,3,4,5.
The other is marked 0,1,2,7,8,9.
Don't ask me how you get 6!

Nevermind getting a silly combination like 38,
but how would you display, say 22, 23, 24 or 25???

Two dices are marked with numbers from zero to nine on each face.
The two dices are meant to display all the dates in a month from 01 to 31.
Remember, single digit dates would have to be shown as 01, 02, 03 etc.
That is, one dice should show zero and the other 1 or 2 or 3 and so on.
The two dices can be interchanged i.e. placed in any order.
What would be the numbers written on the six faces of the two dices???

oh yes, we did....Maybe we started the same time, but you finished earlier.

10 raised to the power 6 is 1,000,000.
We say Logarithm of 1,000,000 to the base 10 is 6.
if a^b=c
(read as a raised to the power b equals c)
then, Logarithm of c to the base a is b.
In short, we say log(to the base a)  c = b
Common logarithm uses the base 10,
Natural logarithm uses the base 'e'.
Logarithms, discovered by John Napier, makes calculations far easier.
Multiplying two numbers is simply adding their logarithms (to the same base).
For example, logarithm value (to base 10) of a few numbers are given.
log 2 = 0.30103
log 3 = 0.47712
log 7 = 0.8451
log 10 = 1
and so on.

You maybe right, I'm not too sure,
but I wanted that to be done without a computer.
And the last digit is 7.
Moreoever, I wanted only the last digit.
There's a pattern which makes it easy to tell.

Anyhow, than you, dear member, for first helping out with the
last 5 digits of 2^500 and 2^2500.