5 helps with everything
Number ending in 0 (5+5)
Number ending in 1 (3x12+5) 41 highest
Number ending in 2 (12)
Number ending in 3 (18+5)
Number ending in 4 (12+12)
Number ending in 5 (5)
Number ending in 6 (3 x 12 or 2 x 18)
Number ending in 7 (5+12)
Number ending in 8 (18)
Number ending in 9 (2 x 12 + 5)
Then the next number ending in 0 can be generated by adding 5+5 and similar for all numbers.
"
Chris Smith,
Friday, March 1, 2024
"The answer to your puzzle is the Frobenius Number for 5,12,18. Wolfram Alpha has a widget for that:
It tells me that 31 is the largest number that can’t be made and I can prove that there are none higher:
32 is ‘12,5,5,5,5’
33 is ‘18,5,5,5’
34 is ‘12,12,5,5’
35 is ‘5,5,5,5,5,5,5’
36 is ‘18,18’
Now that we have five in a row that are possible I can simply keep adding 5 to each of these numbers forever to obtain every number from 32 onwards!"
Rick,
Saturday, March 2, 2024
"The number cannot end in 0 or 5, since that could be paid for with a multiple of 5 egg baskets.
Any number greater than 31 ending in 1 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 2 ending in 2 can be paid with a multiple of 12 and 5 egg baskets.
Any number greater than 13 ending in 3 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 14 ending in 4 can be paid for with a multiple of 5 and 12 egg baskets.
Any number greater than 16 ending in 6 can be paid with a multiple of 5 and 12 egg baskets.
Any number greater than 7 ending in 7 can be paid for with a multiple of 5 and 12 egg baskets.
Any number greater than 8 ending in 8 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 19 ending in 9 can be paid for with a multiple of 5 and 12 egg baskets.
This leaves 31 as the highest number that cannot be paid for with the baskets."
Søren,
Wednesday, March 6, 2024
"Hi there
My students - 4th grade - tried combinations for different numbers and concluded that 31 is the largest number that you can’t make from the three basket sizes.
Kevin Wallis,
Friday, March 1, 2024
"Good morning/evening
I think the answer is 31.
5 helps with everything
Number ending in 0 (5+5)
Number ending in 1 (3x12+5) 41 highest
Number ending in 2 (12)
Number ending in 3 (18+5)
Number ending in 4 (12+12)
Number ending in 5 (5)
Number ending in 6 (3 x 12 or 2 x 18)
Number ending in 7 (5+12)
Number ending in 8 (18)
Number ending in 9 (2 x 12 + 5)
Then the next number ending in 0 can be generated by adding 5+5 and similar for all numbers. "
Chris Smith,
Friday, March 1, 2024
"The answer to your puzzle is the Frobenius Number for 5,12,18. Wolfram Alpha has a widget for that:
"Find Your Frobenius"
It tells me that 31 is the largest number that can’t be made and I can prove that there are none higher:
32 is ‘12,5,5,5,5’
33 is ‘18,5,5,5’
34 is ‘12,12,5,5’
35 is ‘5,5,5,5,5,5,5’
36 is ‘18,18’
Now that we have five in a row that are possible I can simply keep adding 5 to each of these numbers forever to obtain every number from 32 onwards!"
Rick,
Saturday, March 2, 2024
"The number cannot end in 0 or 5, since that could be paid for with a multiple of 5 egg baskets.
Any number greater than 31 ending in 1 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 2 ending in 2 can be paid with a multiple of 12 and 5 egg baskets.
Any number greater than 13 ending in 3 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 14 ending in 4 can be paid for with a multiple of 5 and 12 egg baskets.
Any number greater than 16 ending in 6 can be paid with a multiple of 5 and 12 egg baskets.
Any number greater than 7 ending in 7 can be paid for with a multiple of 5 and 12 egg baskets.
Any number greater than 8 ending in 8 can be paid for with a multiple of 5 and 18 egg baskets. Any number greater than 19 ending in 9 can be paid for with a multiple of 5 and 12 egg baskets.
This leaves 31 as the highest number that cannot be paid for with the baskets."
Søren,
Wednesday, March 6, 2024
"Hi there
My students - 4th grade - tried combinations for different numbers and concluded that 31 is the largest number that you can’t make from the three basket sizes.
Are they correct? "