Wednesday

September 17, 2014

September 17, 2014

Posted by **Ian** on Friday, March 29, 2013 at 12:45am.

Details and assumptions

abcŻŻŻŻŻ means 100a+10b+1c, as opposed to a×b×c. As an explicit example, for a=2,b=3,c=4, abcŻŻŻŻŻ=234 and not 2×3×4=24.

- Maths -
**Wayne**, Friday, March 29, 2013 at 10:20amab = 75

Archaic solution: only possibilities for ab are 01 through 99. Eliminate all of those not divisible by 5, which leaves: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. 60, 65, 70, 75, 80, 85, 90, and 95. Eliminate those not divisible by 3 (divisibility rule for 3) , which leaves 15, 30, 45, 60, 75, and 90. Now eliminate those not divisible by 7, which leaves ab = 75. Divisibility rule for 7: double the last digit and subtract from the remaining digits. If the ramaining digits are divisible by 7, then the original number is divisible by 7. So, our number is 12075. 5 + 5 =10. Subtracting: 1207 - 10 = 1197. 1197mod7 has no remainder, thus our solution.

**Answer this Question**

**Related Questions**

Maths - How many three digits numbers N=abc are there such that a≤b and c...

Algebra - a and b are digits such that \overline{120ab} is a multiple of 3, 5 ...

mahts - Triangle ABC has area [ABC]=468. D,E and F are the midpoints of BC,CA ...

Maths - Find the number of pairs of non-negative integers (n,m), such that 1&#...

MATHS - Find the largest possible integer n such that there exists a non-...

Maths - ABC is a right angled triangle with ∠ABC=90∘ and side ...

maths - Consider the following system of inequalities: {(c−1)x^2+2cx+c+4&#...

MAths - Consider the following system of inequalities: (c−1)x^2+2cx+c+4&#...

MAths - Consider a digital clock. The first time after midnight when the three ...

maths - How many functions f from the reals to the reals are there, such that f(...