This problem solving activity has an algebra focus.
Billie is designing, making and selling number plates.
Each can have a maximum of six characters, numbers or letters.
Billie cannot use plus and minus signs, or any other mathematical symbols.
He can make 10 by using ‘10’ or by ‘TEN’.
In how many ways can he make 12?
What number less than 20 can be represented in the most ways?
This is an open problem in which students have the opportunity to find many creative solutions using their number knowledge and their knowledge of language.
Examples include 4B4TEN for number 6, TEKAU or CINQX2 for number 10. See the solution for a range of examples.
Billie is designing, making and selling number plates. Each can have a maximum of six characters, numbers or letters. Billie cannot use plus and minus signs, or any other mathematical symbols. He can make 10 by using ‘10’ or by ‘TEN’.
In how many ways can he make 12?
What number less than 20 can be represented in the most ways?
Work in a base other than 10, using B for ‘base’.
This is an open problem for which there are very many solutions.
For example:
Number plates for TWO (devised by Aaron Holden a year 8 student from Waiwera South). Are there any other ways to make two?
TWO, 2, II, TO, TOO,
8OVER4, 6OVER3, 4OVER2, 2OVER1,
97B499, 96B498, 95B497, 94B496, 93B495, 92B494, 91B493, 90B492, 89B491,
88B490, 87B489, 86B488, 85B487, 84B486, 83B485, 82B484, 81B483, 80B482,
79B481, 78B480, 77B479, 76B478, 75B477, 74B476, 73B475, 72B474, 71B473,
70B472, 69B471, 68B470, 67B469, 66B468, 65B467, 64B466, 63B465, 62B464,
61B463, 60B462, 59B461, 58B460, 57B459, 56B458, 55B457, 54B456, 53B455,
52B454, 51B453, 50B452, 49B451, 48B450, 47B449, 46B448, 45B447, 44B446,
43B445, 42B444, 41B443, 40B442, 39B441, 38B440, 37B439, 36B438, 35B437,
34B436, 33B435, 32B434, 31B433, 30B432, 29B431, 28B430, 27B429, 26B428,
25B427, 24B426, 23B425, 22B424, 21B423, 20B422, 19B421, 18B420, 17B419,
16B418, 15B417, 14B416, 13B415, 12B414, 11B413, 10B412, 9B411, 8B410,
7B49, 6B48, 5B47, 4B46, 3B45, 2B44, 1B43, 0B42,
2BY1, 1BY2.
Number plates for THREE (devised by Samantha Bucky, from Dunedin North Intermediate). Are there any other ways to make three?
THREE, THR33, NO3, N03, THWEE, NUMBA3, NOIII
1PLUS2, 2PLUS1, 0PLUS3, 3PLUS0, 0PLUS3, 3PLUS0, 1AND2, 2AND1, 3AND0, 0AND3,
THR3E, THRE3,
3BY1, 1BY3, 3X1, 1X3,
9MNUS6, 8MNUS5, 6MNUS3, 7MNUS4, 5MNUS2,
III, IIANDI,
9TAKE6, 8TAKE5, 7TAKE4, 6TAKE3, 4TAKE1, TAKE0,
1ADD2, 2ADD1,
TORU, TROIS, DREI, TRE, TRES.
Number plates for FOUR (devised by Room 1 at Greenmeadows Intermediate School Manurewa.) Are there any other ways to make four?
FOUR, 4, 04, 004, 0004, 00004, 000004, O4, OO4, OOO4, OOOO4, OOOOO4, FOURS, FOURZ, FOUR4, 4FOUR, 4FOUR4, 2PLUS2, 1PLUS3, 3PLUS1, 6B4TEN, 6B410, 5B49, 4B48, 3B47, 2B46, 1B45, 0B44, ONEB45, TWOB46, 2B4SIX, 7B411, 8B412, 9B413, 10B414, 11B415, 12B416, 13B417, 14B418, 15B419, 16B420, 17B421, 18B422, 19B423, 20B424, 21B425, 22B426, 23B427, 24B428, 25B429, 26B430, 27B431, 28B432, 29B433, 30B434, 31B435, 32B436, 33B437, 34B438, 35B439, 36B440, 37B441, 38B442, 39B443, 40B444, 41B445, 42B446, 43B447, 44B448, 45B449, 46B450, 47B451, 48B452, 49B453, 50B454, 51B455, 52B456, 53B457, 54B458, 55B459, 56B460, 57B461, 58B462, 59B463, 60B464, 61B465, 62B466, 63B467, 64B468, 65B469, 66B470, 67B471, 68B472, 69B473, 70B474, 71B475, 72B476, 73B477, 74B478, 75B479, 76B480, 77B481, 78B482, 79B483, 80B484, 81B485, 82B486, 83B487, 84B488, 85B489, 86B490, 87B491, 88B492, 89B493, 90B494, 91B495, 92B496, 93B497, 94B498, 95B499, 4OVER1, 4OVA1, 2TIME2, 4TIME1, Q4, QQ4, QQQ4, QQQQ4, QQQQQ4, 8MNUS4, 7MNUS3, 6MNUS2, 5MNUS1, 4MNUS0, 9MNUS5, 8MNU54, 7MNU53, 6MNU52, 5MNU51, 4MNU50, 9MNU55, 4TH, FOURTH, IV, 4AFTR0, 3AFTR1, 2AFTR2, 1AFTR3, 0AFTR4, 8DVD2, 12DVD3, 16DVD4, 4DVD1, 20DVD5, 24DVD6, 28DVD7, 32DVD8, 36DVD9, 2X2, 4X1, FOURSS, FOURZZ, 444444, 44, 444, 4444, 44444, FOR, FORS, FORZ, FORSS, FORZZ, FORSSS, FORZZZ, 3ADD1, 1ADD3, 2ADD2, FO_UR, F_OUR, F_OU_R, FO_U_R, F_O_UR, _FOUR_, _FOUR, FOUR_, F_O_R, _F_O_R, F_O_R_, FO_R, F_OR, _FOR, FOR_, _FOR_, F0UR, F0R, 4F0UR4, 4F0R4, 4F0UR4, 4F0R, F0R4, F0UR4, 4F0UR
Number plates for FIVE (devised by Adam Collins, from Dunedin North Intermediate.) Are there any other ways to make five?
5, 05, O5,
FIVE, F1VE, FIV3, F1V3, FIVE5, F1VE5, FIV35, F1V35,
HALF10, HALF1O, HLF10, HLF1O,
4PLUS1, 3PLUS2, 2PLUS3, 1PLUS4, 5PLUS0, 5PLUSO, 0PLUS5, OPLUS5,
4ADD1, 3ADD2, 2ADD3, 1ADD4, 5ADD0, 5ADDO, 0ADD5, OADD5,
SINCO, S1NCO, SINC0, S1NC0, RIMA, R1MA,
RIMA5, R1MA5, 5RIMA, 5R1MA,
NUMBA5, NUMBR5, NO5, N05,
V, IADDIV, IVANDI,
5BY1, 1BY5, 5TIMES, 5T1MES,
000005, 00005, 0005, 005, 05,
OOOOO5, OOOO5, OOO5, OO5, O5,
HI5, TAKE5, TAK35,
1B46, 2B47, 3B48 ... (and on to 94B499)
Number plates for SIX (devised by Room 26 at Ellerslie School.) Are there any other ways to make six?
6, 06, 006, 0006, 00006, 000006,
O6, OO6, OOO6, OOOO6, OOOOO6,
VI, SIX, 6OVER1,
3PLUS3, 2PLUS4, 5PLUS1, 4PLUS2, 1PLUS5, 6PLUS0, 0PLUS6,
3BY2, 2BY3, 6BY1, 1BY6, HALF12,
9TAKE3, 8TAKE2, 8SUB2, 14SUB8, 7SUB1, 13SUB7,
7TAKE1, 10SUB4, 11SUB5, 12SUB6, 15SUB9, 5AND1, 1B47, 1AND5, 6AND0, ONEB47,
6X1, 1X6, 2X3, 3X2,
SECHS, ONO, ZES, SES, ALTI, SEKS, ANIM, ENAM, SEIS, LIX, SEI, CHA, CHWECH, SITA, SASE, KUUS, KUUSI, ISII,
1ADD5, 5ADD1, 2ADD4, 4ADD2, 3ADD3, 6ADD0, 0ADD6, OADD6, 6ADD0
1B47, 2B48, 3B49 ... (and on to 93B499)
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/number-plates at 8:56pm on the 26th February 2024