a base-20 notation. Their teacher, William Bartley, guided them. After brainstorming, the students came up with several qualities that an ideal system would have: Visual simplicity: The symbols should be "easy to remember" Iconicity: There should be a "clear relationship between the symbols and their meanings" Efficiency: It should be "easy to write" the symbols, and they should be able to be "written quickly" without lifting the pencil from the paper Distinctiveness: They should "look very different from Arabic numerals," so there would not be any confusion between notation in the two systems Aesthetics: They should be pleasing to look at In base-20 positional notation, the number twenty is written with the digit for 1 followed by the digit for 0. The Iñupiaq language does not have a word for zero, and the students decided that the Kaktovik digit 0 should look like crossed arms, meaning that nothing was being counted. When the middle-school pupils began to teach their new system to younger students in the school, the younger students tended to squeeze the numbers down to fit inside the same-sized block. In this way, they created an iconic notation with the sub-base of 5 forming the upper part of the digit, and the remainder forming the lower part. This proved visually helpful in doing arithmetic. Computation Abacus The students built base-20 abacuses in the school workshop. These were initially intended to help the conversion from decimal to base-20 and vice versa, but the students found their design lent itself quite naturally to arithmetic in base-20. The upper section of their abacus had three beads in each column for the values of the sub-base of 5, and the lower section had four beads in each column for the remaining units. Arithmetic An advantage the students discovered of their new system was that arithmetic was easier than with the Arabic numerals. Adding two digits together would look like their sum. For example, 2 + 2 = 4 is + = It was even easier for subtraction: one could simply look at the number and remove the appropriate number of strokes to get the answer. For example, 4 − 1 = 3 is − = Another advantage came in doing long division. The visual aspects and the sub-base of five made long division with large dividends almost as easy as short division, as it didn't require writing in subtables for multiplying and