There is only 1 j in the puzzle picture.
There are only 6 words on my reduced list that have a j and 2 of these have a t in them.
Now if the one seed word that has a j in it happens to be one of the j-words that also has a t, our word list suddenly goes down to 186 words...
If the j-word is just the only q-word on the list that works is equip
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UPDATE: 10 of the words are four letters and 2 are 3 letters long. This reduces my list to 126 words, which are:
act age aim atom aunt auto cage camp can case cash cat chat chef coin come cost cup cute east echo egg face fame fan fat fee fine fish fit foam fog foot fun gain game gap gas gasp gate gift goat gun hat hen high hint hip home hope host huge hunt ice icon inch into item join jump just main man mass math mean meat menu mesh miss moon much must name nest net nice nose note nut off once one open pact page pass path pen pet pig pigeon pipe poem poet post push put quit safe same scan sea seat ship shoe shop sign sing snap sniff soap soft song soon soup spin spot stem step such suit sun unit upon use
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Since there is only one q, the q-word is quit
But there is also only one t and we used it up in this word, so the list should remove all other words that have a t
But now I must pay attention to my kids. Hopwle this helps somebody solve it.
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I really want you find the answer. It's interesting to read the way you're thinking
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