iNTELLIGENCE

IQ solution to: Venusians Counting

The Venusian has 68 children, 31 sons and 37 daughters. He counts with his 7 antennae and uses the digits 0, 1, 2, 3, 4, 5, 6.

2 + 3 couldn’t be more than 5 in any numbering system. Therefore, there is no carryover in the Venusian addition 4 + 5 = 12. 4 + 5 is 9 in terrestrial numbers, but this is 12 for Venusians. If we say 12, then 1 is 10 fingers, and 2 has to be added. The same is true for the Venusian: If he says 12, 1 is the number of his antennae, plus 2. This is 9 for us. Obviously, the Venusian has 7 antennae.

When he mentions his 43 sons, this means that he has 4 times more sons than antennae, plus 3, i.e. 4 × 7 + 3 = 31. Counting the same way, he has 5 × 7 + 2 = 37 daughters.

A mathematical solution of this problem is

(4a + 3) + (5a + 2) = a² + 2a + 5, a: number of antennae.

The table sums up the corresponding numbers in venusian (V) and terrestrian (T) counting systems.

V	T	V	T	V	T	V	T	V	T	V	T	V	T
0	0	13	10	26	20	42	30	55	40	101	50	114	60
1	1	14	11	30	21	43	31	56	41	102	51	115	61
2	2	15	12	31	22	44	32	60	42	103	52	116	62
3	3	16	13	32	23	45	33	61	43	104	53	120	63
4	4	20	14	33	24	46	34	62	44	105	54	121	64
5	5	21	15	34	25	50	35	63	45	106	55	122	65
6	6	22	16	35	26	51	36	64	46	110	56	123	66
10	7	23	17	36	27	52	37	65	47	111	57	124	67
11	8	24	18	40	28	53	38	66	48	112	58	125	68
12	9	25	19	41	29	54	39	100	49	113	59	126	69

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iNTELLIGENCE

IQ solution to: Venusians Counting

V	T	V	T	V	T	V	T	V	T	V	T	V	T
0	0	13	10	26	20	42	30	55	40	101	50	114	60
1	1	14	11	30	21	43	31	56	41	102	51	115	61
2	2	15	12	31	22	44	32	60	42	103	52	116	62
3	3	16	13	32	23	45	33	61	43	104	53	120	63
4	4	20	14	33	24	46	34	62	44	105	54	121	64
5	5	21	15	34	25	50	35	63	45	106	55	122	65
6	6	22	16	35	26	51	36	64	46	110	56	123	66
10	7	23	17	36	27	52	37	65	47	111	57	124	67
11	8	24	18	40	28	53	38	66	48	112	58	125	68
12	9	25	19	41	29	54	39	100	49	113	59	126	69

V	T	V	T	V	T	V	T	V	T	V	T	V	T
0	0	13	10	26	20	42	30	55	40	101	50	114	60
1	1	14	11	30	21	43	31	56	41	102	51	115	61
2	2	15	12	31	22	44	32	60	42	103	52	116	62
3	3	16	13	32	23	45	33	61	43	104	53	120	63
4	4	20	14	33	24	46	34	62	44	105	54	121	64
5	5	21	15	34	25	50	35	63	45	106	55	122	65
6	6	22	16	35	26	51	36	64	46	110	56	123	66
10	7	23	17	36	27	52	37	65	47	111	57	124	67
11	8	24	18	40	28	53	38	66	48	112	58	125	68
12	9	25	19	41	29	54	39	100	49	113	59	126	69

V	T	V	T	V	T	V	T	V	T	V	T	V	T
0	0	13	10	26	20	42	30	55	40	101	50	114	60
1	1	14	11	30	21	43	31	56	41	102	51	115	61
2	2	15	12	31	22	44	32	60	42	103	52	116	62
3	3	16	13	32	23	45	33	61	43	104	53	120	63
4	4	20	14	33	24	46	34	62	44	105	54	121	64
5	5	21	15	34	25	50	35	63	45	106	55	122	65
6	6	22	16	35	26	51	36	64	46	110	56	123	66
10	7	23	17	36	27	52	37	65	47	111	57	124	67
11	8	24	18	40	28	53	38	66	48	112	58	125	68
12	9	25	19	41	29	54	39	100	49	113	59	126	69