# continental divide

By xi’an

(This article was first published on R – Xi’an’s Og, and kindly contributed to R-bloggers)

While the Riddler puzzle this week was anticlimactic, as it meant filling all digits in the above division towards a null remainder, it came as an interesting illustration of how different division is taught in the US versus France: when I saw the picture above, I had to go and check an American primary school on-line introduction to division, since the way I was taught in France is something like that

with the solution being that 12128316 = 124 x 97809… Solved by a dumb R exploration of all constraints:

```for (y in 111:143)
for (z4 in 8:9)
for (oz in 0:999){
z=oz+7e3+z4*1e4
x=y*z
digx=digits(x)
digz=digits(z)
if ((digz[2]==0)&(x>=1e7)&(x=1e3)&(digz[4]*y9)&(r1=1e2)&(7*y=1e2)&(r2=1e2)&(digz[3]*y9)&(r3
Looking for a computer-free resolution, the constraints on z exhibited by the picture are that (a) the second digit is 0 and the fourth digit is 7.  Moreover, the first and fifth digits are larger than 7 since y times this digit is a four-digit number. Better, since the second subtraction from a three-digit number by 7y returns a three-digit number and the third subtraction from a four-digit number by ny returns a two-digit number, n is larger than 7 but less than the first and fifth digits. Ergo, z is necessarily 97809. Furthermore, 8y
Filed under: Books, Kids, pictures, R Tagged: arithmetics, division, FiveThirtyEight, long division, The Riddler