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Omid
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How many odd numbers are there between 3000 and 7000, NO REPEAT?
My answer is 1232 which is wrong according to the solutions manual.
My answer is 1232 which is wrong according to the solutions manual.
Omid said:How many odd numbers are there between 3000 and 7000, NO REPEAT?
My answer is 1232 which is wrong according to the solutions manual.
Your solution looks eager and completely new to me. But the answer in the book is this:xanthym said:{Valid Permutations Between 3000 & 7000} = 1008
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vsage said:(might be good if he posted what he did so I can know what not to repeat)
Consider the case 3000-3999. Any number fitting the scheme above will be expressed as (3)(0, 1, 2, 4, 5, 6, 7, 8, 9)(0, 2, 4, 5, 6, 7, 8, 9)(7, 9) where I assumed 1 was the hundreds digit and 5 was the tens digit (so 1 was deleted from the selection of possible tens digits and 1 and 5 were deleted from the selection of unit and tens). Multiply the number above by 2 for the assumptions made about the units digit and by 1 for the assumptions made about the units digit to get the answer for that range 3000-3999. This should be the same answer for 5000-5999 (I get 288), and a similar method can be used to find the case for 4000-4999.
In case you're wondering about the pretty arbitrary way I wrote that, multiply the number of numbers inside each parenthesis to get the total number of permutations, and then multiply again by the number of choices I said I deleted for the units and tens digits.
I hope this made sense: I'm a little stumped how to explain it. Edit: I get a solution that's about 200 lower than what you listed.
Healey01 said:This I checked by brute force, not mathematics.
To determine the number of odd numbers between 3000 and 7000, we can use the formula (last number - first number) / 2. In this case, it would be (7000 - 3000) / 2 = 2000.
Yes, the list of odd numbers between 3000 and 7000 is: 3001, 3003, 3005, 3007, 3009, 3011, 3013, 3015, 3017, 3019, 3021, 3023, 3025, 3027, 3029, 3031, 3033, 3035, 3037, 3039, 3041, 3043, 3045, 3047, 3049, 3051, 3053, 3055, 3057, 3059, 3061, 3063, 3065, 3067, 3069, 3071, 3073, 3075, 3077, 3079, 3081, 3083, 3085, 3087, 3089, 3091, 3093, 3095, 3097, 3099, 3101, 3103, 3105, 3107, 3109, 3111, 3113, 3115, 3117, 3119, 3121, 3123, 3125, 3127, 3129, 3131, 3133, 3135, 3137, 3139, 3141, 3143, 3145, 3147, 3149, 3151, 3153, 3155, 3157, 3159, 3161, 3163, 3165, 3167, 3169, 3171, 3173, 3175, 3177, 3179, 3181, 3183, 3185, 3187, 3189, 3191, 3193, 3195, 3197, 3199, 3201, 3203, 3205, 3207, 3209, 3211, 3213, 3215, 3217, 3219, 3221, 3223, 3225, 3227, 3229, 3231, 3233, 3235, 3237, 3239, 3241, 3243, 3245, 3247, 3249, 3251, 3253, 3255, 3257, 3259, 3261, 3263, 3265, 3267, 3269, 3271, 3273, 3275, 3277, 3279, 3281, 3283, 3285, 3287, 3289, 3291, 3293, 3295, 3297, 3299, 3301, 3303, 3305, 3307, 3309, 3311, 3313, 3315, 3317, 3319, 3321, 3323, 3325, 3327, 3329, 3331, 3333, 3335, 3337, 3339, 3341, 3343, 3345, 3347, 3349, 3351, 3353, 3355, 3357, 3359, 3361, 3363, 3365, 3367, 3369, 3371, 3373, 3375, 3377, 3379, 3381, 3383, 3385, 3387, 3389, 3391, 3393, 3395, 3397, 3399, 3401, 3403, 3405, 3407, 3409, 3411, 3413, 3415, 3417, 3419, 3421, 3423, 3425, 3427, 3429, 3431, 3433,