PART 2
For FLOCK * 7 = GEESE, the answer is:
F=1, L=0, O=9, C=4, K=8, G=7, E=6, S=3
Explanation:
F can only be 1 to maintain the number of digits, therefore, G=7/8/9 and L=0/2/3/4
Since 7 is odd, we can produce numbers with patterns 700#0, 711#1, 722#2, etc. until 988#8.
I started with 700#0. We can establish 70000 and 70070 are divisible by 7. If we keep adding either 70 or 1071 (which is 7 * 53) as needed, we can establish the pattern:
70000, 70070, 71141, 72212, 72282, 73353, 74424, 74494, 75565, 76636, 77707, 77777, 78848, 79919, 79989
Finding the next number divisible by 7 with the format 800#0 and continuing the pattern, we get:
80010, 80080, 81151, 82222, 82292, 83363, 84434, 85505, 85575, 86646, 87717, 87787, 88858, 89929, 89999
With 900#0, we get
90020, 90090, 91161, 92232, 93303, 93373, 94444, 95515, 95585, 96656, 97727, 97797, 98868, 99939
Removing the ones with:
- 1s on any digit,
- repeated tens digit,
- repeated ten-thousands digit,
- 0s formatted 7####,
- 2s formatted 8####, and
- 3s or 4s formatted 9####
We get:
72282, 73353, 74424, 74494, 75565, 76636, 78848, 79989, 80080, 82292, 83363, 84434, 85505, 85575, 86646, 89929, 90020, 90090, 95585, 96656, 97727, 98868
I tried dividing it all by 7 and the only working solution is
10948 * 7 = 76636