1	2	3	4	5	6	7	8	9	10
11	12	13	14	15	16	17	18	19	20
21	22	23	24	25	26	27	28	29	30
31	32	33	34	35	36	37	38	39	40
41	42	43	44	45	46	47	48	49	50
51	52	53	54	55	56	57	58	59	60
61	62	63	64	65	66	67	68	69	70
71	72	73	74	75	76	77	78	79	80
81	82	83	84	85	86	87	88	89	90
91	92	93	94	95	96	97	98	99	100

A part of mathematics that we do not study in depth in high school is called number theory. The following simple arithmetic game is based on simple number theory principles of addition / subtraction of odd/even integers. Click here to play the game. Play it as many times as necessary to try and figure out the winning strategy. Resist the temptation to click on the winning strategy link or scrolling down to the winning strategy. After figuring out the winning strategy or 20 minutes which ever comes first, answer the following questions:

1. Write the resulting integer types when adding/ subtracting odd and even integers.

For example: odd + odd = even

2. Are there any numbers that the computer started with in which it was impossible for you to win the game? Explain why?

3. In programming there is an operator called modulus usually written as the symbol %. This operator will give the remainder of a division. For example, 7%5, read as 7 modulus 5 is equivalent to 2 because 7 divided by 5 is 1 with a remainder of 2. Similarly 18 % 7( 18 modulus 7 ) is 4, because 18 divided by 7 is 2 with a remainder of 4. What modulus operation is the computer using to determine whether a number is odd or even to determine the its next move? In other words, what would be the indication to the “computer” the number displayed is odd or even?

http://www.cut-the-knot.org/SimpleGames/Aliquot.shtml