Knowing that each letter corresponds to a single digit, find out which digit does each letter represent.

Hint Adding what digit seven times gives a sum that ends in 9?

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# Month: February 2018

Daily morsels of math

Knowing that each letter corresponds to a single digit, find out which digit does each letter represent.

Hint Adding what digit seven times gives a sum that ends in 9?

Let ABC be a scalene triangle. Extend side BC at both ends such that BD = AB and CE = AC. In triangles ABD and ACE draw perpendiculars BF and CG, and let J be the intersection of BF and CG. Is AJ the bisector for angle BAC?

Hint Show that <BDJ ≡ <BAJ, <CAJ ≡ <CEJ, <BDJ ≡ <CEJ.

A number is divisible by 3 if the sum of the digits is divisible by 3. How about a number of the type (2^{2n} – 1), where n is a positive integer? Can we show that it is always divisible by 3?

Hint No need to use divisibility by 3 rule here, but a particular factoring rule: a^{n}– 1 = (a – 1)(a^{n-1}+ a^{n-2}+ … + a + 1).