`http://www.botik.ru/~duzhin/UGP/111-3.html`

`http://www.mtholyoke.edu/~schmutov/artest/111-3.html`

According to V.I.Arnold [1], everybody should be able to divide 111 by 3 without a calculator. In October 2000, the present authors conducted a test with the students of mathematics in two small universities in the US and Russia (Mount Holyoke College, Mass. and University of Pereslavl, Pereslavl-Zalessky). We announced that we were going to have a public opinion poll. Every student was given a folded piece of paper with the question ``'' and asked to write the answer in secret from the others.

Results follow.

University | Course/Year | Number of Students | Number of Answers: Correct/Blank/Wrong | All Wrong Answers |

Mt. Holyoke | ``Linear algebra'' (2, 3, 4 years) | 24 | 22/0/2 |
; 111 : 3 = 21 |

Mt. Holyoke | ``Calculus 1'' (1st year) | 9 | 7/0/2 |
(periodic decimal); . |

Pereslavl | ``General Algebra'' (3rd year) | 16 | 10/2/4 | 111 : 3 = 1; ; 111 : 3 = 33.61; 111 : 3 = 111 n : 3n, where
. |

Pereslavl | '`Computational Geometry'' (4th year) | 11 | 9/2/0 |

*Remarks.*

1. The answer 111*n*:3*n*, where
,
is consonant
with the famous Arnold's story [1] about the French boy who was
asked to add 2 and 3 (his answer was ``2+3=3+2, because addition
is commutative'').

2. A probable reason why letter `l' appeared in one of the answers: the student mistook the last `1' of 111 for `l' because of teacher's handwriting.

The table suggests that nowadays typical American students know mathematics a little better than their Russian counterparts. Is it a sign of decline of the Russian school mathematical education?

**References.**

[1] ``Californian wars in Dubna''. V.I.Arnold interviewed by E.Kokurina. -- ``Obshchaya gazeta'', no. 38, September 21, 2000 (in Russian). Text and PostScript files available on-line.