The number of lollipops in a box is between 60 and 100. If they are put into packets of 3, there will be 1 lollipop left. If they are put into packets of 5, there will be 1 lollipop left. If they are put into packets of 7, there will be no lollipop left. How many lollipops are there in the box?
First, I draw a table to analyse the remainders when divided by 3, 5 and 7. [using heuristics H02 and H03]. The question asks for a number with remainders (1, 1, 0). However, we can SHIFT the problem. [H09] If we consider one less than the required number, the remainders are (0, 0, 6). We look for a number with such a profile.
Having zero remainders under division by 3 and by 5, this number must be a multiple of 15. Trying 15 [H07], I get (0, 0, 1) because 15 = 2´14+1. To get a remainder-profile of (0, 0, 6), I multiply by 6, and I get 15´6 = 90. Now I just SHIFT back 1 to get the required answer!
List of Heuristics Used
In solving this question, I did not really use any Chinese Remainder Theorem or advanced mathematics. I merely used heuristics that can be understood by most people, including the parents helping them and the teachers marking the test scripts. J
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